The word “derivatives” is no longer strange vocabulary even for someone unfamiliar with the financials industry. Derivatives include the totality of the financial tools connected to futures and options, and for outsiders, they conjure the image of something highly mathematical and hard to understand. Due to their complex façade, derivatives are often treated like monsters and blamed for market catastrophes.

The title of this chapter actually has a double meaning. The first meaning is an obvious one: the chapter literally talks about market impact due to derivative instruments, which not only include futures and options but also broader instruments such as ETFs and index‐related strategies. The second meaning is that subjects covered here may not be mainstream topics; in other words, as general investors seek investment strategies in Japanese equities, these subjects may not seem as important as more traditional subjects.

If these subjects are not as important as more traditional ones, then the question is whether these subjects are “noise.” The answer is that these are “noise” sometimes but not other times. Put differently, whether “noise” or not depends on how they are used. The essence of this statement hopefully will become clearer later on, but be that as it may, investors can make their own judgment if, and only if, they know the nature of these subjects.

Even if investors do not trade futures, options, or ETFs, knowing about them should give some theoretical comfort when trading common stocks. At least no one will laugh at knowledgeable investors for not knowing about these subjects. Not only that, but such investors will have acquired some bragging rights for knowing about them, because derivatives simply cannot be ignored when trying to wholly understand the ups and downs of the equity market.

Volatility

“Volatility” is not a strange word even for those unfamiliar with the equity market. Whether in equities, FX, or fixed income instruments, volatility refers to the amount or the rate of change in the price of the underlying financial instruments. In general, volatility is the annualized standard deviation of the daily returns (commonly denoted as σ).

The standard deviation measures how much the numbers deviate from their average, and when the numbers are normally distributed, one standard deviation denotes the probability of the numbers remaining between 1σ and –1σ to be about 68%.

Naturally, the standard deviation depends on the timeframe where the average is taken. Accordingly, volatility of a time series depends on the period of measurements. As a rule, when the short‐term volatility is high, so is the long‐term volatility, but this is just a general tendency. The price movement of financial instruments depends on the economy as well as the era; hence, low one‐month volatility may not necessarily indicate low one‐year volatility.

In the options market, volatility plays a key role. In the Black‐Scholes model, used to price options, volatility is one of the needed variables. Prices of options are determined based on the projected price of the underlying instruments in the future, and obviously future prices depend on their volatility.

It is also obvious that the volatility used to calculate option prices is the projected future volatility. In industry jargon, the projected future volatility is called implied volatility, and is distinguished from historical volatility, which is uniquely calculated from past data. Incidentally, since no one is certain of the future price movement, implied volatility, in most cases, is deduced from some mathematically‐adjusted form of historical volatility.

Let us assume that, in the past, one‐month volatility of the Nikkei 225 was 10%. What does this number mean? Using 20 trading days as one month, the rate of daily change is calculated to be about 0.6%. If the Nikkei 225 was JPY20,000, then if the index oscillated by JPY120 per day, the volatility would be about 10%, and if the index oscillated by 1% (JPY200), then the one‐month volatility would rise to 16.3%.

The average one‐month volatility of the Nikkei 225, calculated from 1990, is 22.2%, and since 2009, after the global financial crisis, the average one‐month volatility is 21.5%. The former number suggests that the Nikkei 225 moved about 1.1% per day, which, when calculated using 20,000 as the base value, leads to JPY220 per day.

For many observers of the Nikkei index, the number may appear puzzling, as the experience tells them that they do not often see the index move by JPY220 per day. The puzzlement stems from the base value, because the Nikkei 225 near JPY20,000 is not realistic. Since 1990, the Nikkei 225 has seldom been above JPY20,000, and accordingly, the 1.1% daily move only meant JPY88 or JPY110.

We also note that the 1.1% daily move is on the average. For example, if the Nikkei 225 moves by 3% per day during just four days out of twenty, and moves 0% for sixteen days, the one‐month volatility rises to above 20%. The impression from the experience—the Nikkei 225 did not move JPY220 per day—therefore seems correct.

Volatility also has some interesting features that general investors should be aware of even if they do not trade options. One: volatility tends to mean‐revert. This feature is probably intuitive. When something changes, the rate of change is not constantly large but generally goes up and down. Equity prices, in particular, unless the underlying companies go bust, tend to fluctuate around certain levels.

Two: volatility tends to rise when the underlying prices fall, and vice versa. A simple reason for this phenomenon is that a drop in the equity price or index generally results from a surprise, while a rise comes as more or less expected. As discussed in the “ISMPMI” section in Chapter 1, this is a reflection of the human psyche and only goes to prove that the equity market is a mirror of human minds.

Remember, when we hear of good news, we seldom act immediately. We are skeptical at first, and only after being reasonably convinced do we act. In other words, humans are suspicious and careful by nature. When we hear of bad news, on the other hand, we tend to act immediately to avoid the risk. Only after we act do we look into the facts, and if the facts are straight, we take comfort; if not, we try to undo the initial action.

When the equity market goes up on good news, the stocks are being bought “carefully,” and thus, the volatility on the upside is more under control. When the equity market goes down on bad news, investors rush to dump stocks to lessen the risk, and thus the volatility on the downside becomes more pronounced.

Needless to say, the above prescription is not 100% foolproof. Indeed, there have been some exceptional cases where the market volatility rose on the upside. One case that comes to mind is from November 2012 to January 2013, when the equity market jumped at the introduction of Abenomics. Another case is the period immediately following the surprising US presidential victory of Donald Trump.

Historical and Implied

As stated in the previous section, volatility can be thought of as either historical or implied. Since historical volatility is calculated from past time series data, it is also known as realized volatility. We also saw that implied volatility is a projected volatility whose calculation, to some extent, is based on volatility in the past.

When we plot implied volatility and historical volatility side by side, we see that implied volatility, in general, rises after and falls before historical volatility. There is a simple reason for this: options traders usually do not foresee a large movement in the stock market before it actually takes place, and thus they customarily react after the fact. Of course, if there is going to be a historical event, such as a US presidential election, then the market is expected to show more than usual movements, and therefore we often observe that implied volatility rises before the fact. A sudden and marked jump in implied volatility, known as a volatility spike, however, generally occurs only after a jump in historical volatility.

Once volatility jumps but is expected to come down in the future, then the implied falls before the historical. This is easily understood from the calculation of volatility, also described in the previous section.

In calculating one‐month volatility, for example, the time series data from the last thirty days is used (assuming 1 month = 30 days). Strictly speaking, since the market is closed on Saturdays and Sundays, the time series data from the last twenty days is used, but the distinction here is beside the point.

If the last thirty‐day time series data is being used, then only the incidents that took place during the thirty‐day period contribute to the calculation. If the market had crashed thirty days earlier, and the realized volatility spiked as a result, then the volatility engendered by the initial market crash is destined to vanish thirty days after (since only thirty days' worth of data contributes to the volatility calculation). Option traders see this decline ahead of the time, and hence implied volatility declines ahead of historical volatility.

Here, I hasten to add that historical volatility is not the sole driver of implied volatility. There exist volatility funds as well as those that trade volatility as an asset. If volatility is traded as an asset, supply‐demand imbalance enters into the equation, and implied volatility is affected by it.

It is not difficult to imagine that forecasting “near future” is easier than “far future.” Accordingly, forecasting near‐term volatility is easier than far‐term volatility. Thus, while near‐term implied volatility is more in line with near‐term historical, far‐term implied is more swayed by other elements.

Near‐term implied volatility is by no means immune from supply‐demand issues but less affected by them, as short‐dated options enjoy greater liquidity. Long‐dated options, on the other hand, often suffer low liquidity and, hence are more impacted by the demand of certain market participants.

In the following sections, we will view how transactions involving derivatives—mainly futures and options—affect the equity market, and how option‐imbedded structures products affect volatility itself.

Futures Influence

The term “present value” should be familiar to anyone in the financial field. Goods or money have “present” and “future” values connected by the interest rate (if equities, add dividends). If the interest rate is positive, the present value will increase with time by the interest paid in the future, so the future value will necessarily be higher. This “future value” is the theoretical price of the futures (in Nikkei 225 or TOPIX futures, the present value will rise relative to the future value by the amount of the dividend paid).

Investors who trade futures can largely be divided into three categories. One group consists of speculators. If speculators believe that a bull market is ahead, they buy (index) futures, and if not, sell (index) futures. In theory, there should not be any arbitrage opportunities between futures and cash (otherwise risk‐free profit would be possible), and thus buying of futures results in higher index value and vice versa, bestowing speculators power to move the market. As discussed in the “BoJ and Kuroda Bazooka” section in Chapter 2, when the market is overheated, often we see cash due to arbitrage trades mount to very high levels. As was the case on May 22, 2013, this is a warning sign.

Another group that actively trades futures are the hedgers. Many domestic institutional investors such as pension funds are among those in this group. They typically manage a considerable size of index funds, and hence if they wish to remain market neutral, they sell index futures against their portfolios. If they sell futures, the cash market will be exposed to downside pressure by the no‐arbitrage principle. Thus, it looks as though the move is ill‐advised. At least in theory, however, the hedge is structured to assure market neutrality, so the concern may be unjustified.

The third group of investors is the arbitragers, and their impact on the cash market is also limited. The future value and present value are related by the simple equation, as explained above, but sometimes the relationship becomes distorted by the demands from speculators and hedgers. Arbitragers try to take advantage of these opportunities.

If arbitragers believe that the futures market price is above the fair theoretical value, they sell futures and buy cash. If the opposite is the case, they sell cash and buy futures to take the spread. In Japan, index futures are settled quarterly on SQ. At that time, the futures price should match the cash price. In other words, the theoretical price matches the market price. Thus, had the futures been sold (bought) when the market price was expensive (cheap), a profit can be generated.

Viewed from the cash market, since futures and cash are traded in opposite directions (buy and sell, or vice versa), the impact of arbitrage activity is limited. Arbitragers have a pronounced impact, instead, on individual stocks. This, in fact, is similar to the impact due to index funds alluded to earlier.

Arbitrage opportunities between futures and cash generally arise based on the market sentiment (bullish or bearish), and interest rate and dividend expectations. To take advantage of arbitrage opportunities, arbitragers must hold a cash equity portfolio that exactly matches the index (whose futures they trade) in names and weights.

As a result, if there is going to be a change in index members, arbitragers need to buy and sell individual stocks based on the expected change. This is where the impact on individual stocks comes from. Since the process is very much similar to index funds, we will look into the details in the next section.

Impact of Index Funds

Index funds manage money by investing in indices, their performance measured either relative to the given indices or by the performance of the indices themselves. Those that measure relative performance are called active funds, and those that offer the performance of the indices themselves are called passive funds.

More narrowly, some call only passive funds “index funds,” but here, in contrast to most hedge funds that offer absolute returns, we call all funds that offer index returns or returns relative to certain indices “index funds.”

The state pension funds that I worked with were index funds, both active and passive. Depending upon country allocations, indices relative to which the investment performance was measured naturally varied. For Japan, as is the case for most US pension funds, the index used was the MSCI Japan Index. For most domestic pension funds in Japan, the index of choice is the TOPIX, though there are some that use the JPX400, Nikkei 225, or others.

The basic approach taken by index funds is to align their portfolio performance to given indices. The measure of alignment is called the tracking error, which is an annualized spread of return between the portfolio and index.

For active funds, their mission is to outperform the given index, but the outperformance generally needs to be kept within a certain range. The reason is that large outperformance necessarily entails large volatility relative to the index, and thus, from the risk‐management point of view, is considered undesirable.

The tracking error, therefore, is important even for active funds, and the returns are expected to remain within the predetermined tracking error. For passive funds, as their desirable performance is the index return, the tracking error needs to be minimized.

If we wish to keep our portfolio in line with a given index, a failsafe way is to purchase all the constituents' stocks in the index according to their weights. Indeed, managers of the passive Nikkei 225 Index fund generally hold all 225 stocks in their portfolios to achieve a 0% tracking error.

For the passive funds that track the MSCI Japan Index, since there are only about 300 stocks in the index, a similar approach may be taken. For the TOPIX, however, since there are more than 1800 stocks in the index and many of the stocks with smaller weights often suffer from limited liquidity, a general approach is just to hold stocks with higher liquidity and adjust their weights in the portfolio to minimize the tracking error.

For the management of active funds, whether the funds track the Nikkei 225 or MSCI Japan, the portfolio managers naturally need not hold all the index constituent stocks. A general approach is to hold a limited number of stocks in the portfolio to keep the tracking error within range and adjust the weights to achieve outperformance over the index. Needless to say, the ability of the portfolio managers is tested in this instance.

What about the impact of index funds on the overall equity market? Notwithstanding the unrealistic case of all equities being held by index funds, the most significant impact is felt by individual stocks.

Let us assume that a large index fund has just been created and that the fund is required to track the Nikkei 225. The fund needs to buy the Nikkei 225 constituents according to their weights in the index, and thus, from a view point of funds flow, the largest beneficiary is the stock with the largest weight in the Nikkei 225 Index, which, as this book was written, is Fast Retailing. The price of the Fast Retailing stock is likely to rise as a result, regardless of the company's business performance. Such is the impact of index‐tracking funds: they can dominate stock price performance in spite of stock fundamentals.

The impact of the GPIF asset allocation change, discussed in Chapter 2, “Policy Impact,” is a typical example of a massive index fund's having tremendous impact on individual stocks. Creation of funds by major insurers or asset managers is publicly available information, and thus, by following the disclosure, we should be able to take a guess at which stocks may be affected and to what degree as a consequence.

The impact of index funds, however, is not limited to those examples. In fact, more measurable impact may be observed at index rebalance. Index rebalance refers to a review and possible alteration of index constituent stocks. The criteria and frequency of the review vary depending on the host of the index, but the aim of this book is not to list the myriad of indices or index rules. Each index has its own rebalance rules and policies, and they are in the public domain.

Those versed in the rules of index reviews can guesstimate which stocks are to be added to or deleted from a given index. The stocks to be deleted will likely suffer from a selloff by index funds and the stocks added will likely gain from a buying activity. If investors can forecast the deletion and addition candidates ahead of a rebalance, then they should be able to make a profit by shorting the deletion and buying the addition candidates. The investment strategy that employs this method is commonly known as the suckerfish investment, and its history goes back quite a way.

Of course, if we could make a profit just by following index rebalance rules, nothing could be simpler. As usual, however, the reality is far more complicated than meets the eye.

First, there is the difficulty of timing. For major indices such as the Nikkei 225, MSCI Japan, and TOPIX, a few months before the actual rebalance date, large brokerage firms have already published index rebalance forecast reports. These reports, closely following the index rebalance rules, forecast stocks to be deleted and added, and estimate the demand from passive funds, translated into the daily transaction volume of each stock. Since the passive demand comes from the world's pension funds and insurers, as well as mutual funds and ETFs, there are naturally some divergences in their forecasts, but most commonly the passive demand is estimated to be less than 10% of the total market capitalization of the index.

Actual reports contain not only the names of deletions and additions, but also the stocks that will likely be most affected by the rebalance. Since every stock in a given index comes with an assigned weight, any alteration among constituent members generates a weight shift, possibly resulting in trades by index funds. The reports, therefore, customarily list affected stocks in the order of impact.

A difficulty in rebalance trades comes first from the suckerfish investors, who establish their positions (by going long on those positively affected and short on those negatively affected) when these reports are initially released. It is also likely that proprietary desks of major securities firms and event funds, which may have their own forecasting methods, have set up similar positions as well.

What these investors want, obviously, is to make a profit, so they do not have to wait until the actual index rebalance takes effect. Rather, it is probable that they close their positions before the event, thereby engendering a large volume of buy‐and‐sell orders. Upon release of index rebalance reports, we often bear witness to a selloff of deletion candidates and buying of addition candidates. For event funds and proprietary traders, these may provide a perfect occasion for unwinding their positions.

Transactions by passive funds generally take place right at the rebalance. This is because passive funds abhor tracking errors, as discussed earlier, and trading days before or after rebalance increases tracking errors. We may think then that we should just pay attention to the passive fund demand and buy or sell stocks accordingly. Actually, this strategy does not work all that well either.

Each stock has its own liquidity, and if someone puts a large bid in for illiquid stocks, the stock prices will likely respond by leaping to higher levels. The result is an increase in tracking error, which passive funds wish to avoid in the first place.

Passive funds commonly employ execution traders, whose primary mission is to ensure smooth trading while minimizing tracking error. Upon rebalance, how they trade deletion and addition names is largely up to the discretion of execution traders, which makes the price movement of these stocks less transparent.

Another source of difficulty in taking advantage of rebalance is the rules of index rebalance themselves. Each index has its own rules, as mentioned before, but the rules are often not clearly defined or even practical.

For the Nikkei 225, for example, a portion of the rules is left up to interpretation by the Nikkei. Likewise, for the MSCI Japan, the MSCI retains its discretion regarding its index rules, and the same is true for the TOPIX, the Tokyo Stock Exchange (TSE). Thus, while strictly going by the rules may allow us to know 90% of the deletion and addition candidates before an actual rebalance, often 10% are missed almost inevitably.

If the member selection rules are rigid, guesstimating deletion and addition candidates becomes a cinch, giving advantage to certain investors. So, index providers intentionally make the rules less transparent. Perhaps more cynically viewed, index providers themselves are not certain about their selection methodology and by inserting “up to our discretion” somewhere in their index rules, they protect themselves from unwanted criticism or even lawsuits.

This second reason is perhaps most apparent in the free‐float‐ratio adjustment. The free‐float‐ratio refers to the ratio of short‐term equity holders to the total equity holders and is important in index reviews because these adjustments are used to determine equity weights in indices such as the MSCI Japan and TOPIX.

Deciding who the short‐term or long‐term equity holders are is not as easy as it sounds, however. If the holder is the original owner of the company or major banks (known as policy stakeholders), then the distinction may be easy, but whether those listed as major shareholders in the company reports are short‐term or long‐term investors is often not clear. Consequently, who are and who are not free‐float investors is determined somewhat whimsically by the index providers, creating much ambiguity in the allocation of equity weights.

We have seen hitherto how index funds and suckerfish investors impact individual stocks, but to benefit from their actions, there are several important hurdles that need to be cleared. Indeed, as far as I know, there is only a handful of very able proprietary and day traders who are successful in taking advantage of the opportunities generated by index rebalance.

Influence of Structured Products

Structured products, to be discussed here, refer to option‐imbedded fixed income instruments, which are commonly created for and sold to retail investors. In Japan, put‐imbedded instruments are the mainstream, and the options are generally written on equity indices, single stocks, and the currency.

The equity index is mostly the Nikkei 225 and single stocks are mostly large‐cap stocks. The structure of the put option is such that the strike is set at 100% of the initial underlying asset price, the knock‐out barrier at 105%–110% of the strike, and the knock‐in barrier is placed somewhere between 40% and 70% of the strike.

For those unfamiliar with option terminology, the “strike” refers to the price of the underlying asset at and beyond which the option can be exercised, the “knock‐out barrier” is the price where the option becomes worthless, and the “knock‐in barrier” is the price level beyond which the option becomes exercisable at the strike price. In the case of structured products, the knock‐out barrier is described in the early redemption clause. The difference between the strike and knock‐in barrier is that the strike is proportional to the value of the option, while the knock‐in barrier is a simple level where the option becomes alive.

Ignoring the option premium for the sake of simplicity, if the strike was set at 100% of the initial asset price and the asset price drops to 80% at expiry of the option, then the value of the put option at expiry will be 20%. If, in addition, the knock‐in barrier was set at 70% simultaneously, the asset price did not reach the barrier, and hence, the option expires worthless. If, on the other hand, the asset price fell to 60% at expiry, the knock‐in barrier was breached, and the value of the put option is 40%.

As seen in these examples, the structure of the option itself is not all that complicated. Nevertheless, structured products can cause havoc in the price movement of the underlying asset. The reason is as follows.

Trading options is a contract between buyers and sellers. In the case of put‐embedded structured products, retail investors buy the instruments in order to attain the income generated from them, which is equivalent to selling the embedded puts (i.e., investors sell puts and receive the premium as income).

The buyers of the put options are the securities firms that originated the structured products. In professional jargon, the retail investors are short‐put and securities firms are long‐put. Since retail investors buy structured products for their income, and since the knock‐in barriers are set well below the strike, either they hold on to their instruments or wait until knock‐out to repurchase similar products.

For securities firms that are on the opposite end, long‐put positions are considered as risk. The reason is that the value of the put options depends on volatility, time to expiry, price of the underlying asset, and so on, so long‐put holders are exposed to daily mark‐to‐market price fluctuations.

The risks obviously need to be hedged. While the risks associated with time and volatility are generally hedged by constructing opposite positions using listed options or over‐the‐counter options (the latter may not be a perfect hedge, however), the risk associated with the price movement of the underlying asset (called the delta [δ] risk) is hedged by trading the underlying asset (for single stocks) or futures of the underlying asset (for currencies and indices). This δ‐hedge activity generates considerable impact on the price of the underlying asset on occasion.

It gets a little complex from here, but to understand the impact of the structured products, we cannot avoid a further complexity. As stated earlier, the value of options depends on elements such as the price and volatility of the underlying asset, time to expiry, and so forth. This means that the value of options possesses certain sensitivity to these elements.

These sensitivities are commonly called Greeks and literally denoted by Greek letters. One of these is the δ, which is the sensitivity to the price of the underlying asset. The δ is generally expressed by how much the option price moves per 1% move in the price of the underlying asset. If, therefore, the underlying asset price moves up by 1% and at the same time the price of the option moves up by 1%, then the δ is 100% or 1.

This number actually is the hedge ratio when the δ risk needs to be hedged. If the option price goes up by 1% when the underlying asset price goes up by 1%, then to hedge the risk (so that the position remains unaffected), the same amount of the underlying asset as the option needs to be sold. If the option price falls by 1%, on the other hand, the opposite needs to be done. Selling or buying an underlying asset according to the δ is called the δ hedge.

More concretely, if we are put‐long on an index, we need to go long on the index futures by the amount specified by the δ. Note that the δ changes according to the change in the underlying asset price. This is because the value of an option is dependent on how far the underlying asset price is from the strike of the option.

Just to fill in a few basics about options, basics that can be found anywhere in textbooks, when the underlying asset price is at the strike of the option, the option is said to be at‐the‐money (ATM), when it is beyond the strike (upside on calls and downside on puts), the option is said to be in‐the‐money (ITM), and when it has not reached the strike, out‐of‐the‐money (OTM).

The value of the put option increases when the underlying asset price falls, and hence, we must increase the hedge ratio in that case and decrease it when the asset price rises. In other words, when the underlying asset price falls, more futures need to be bought, and when the underlying asset price rises, the amount of futures needs to be reduced (the futures need to be sold).

Note that buying index futures when the index falls and selling index futures when the index rises amount to reducing index volatility. This is the same with long‐call positions; in this instance, when the index rises, futures need to be sold (since for long‐calls, futures are shorted for the hedge), and when the index falls, futures need to be bought, thereby once again lessening index volatility. Once this mechanism is understood, it becomes evident that hedging the short‐put or short‐call position will result in increasing volatility.

Let us now think of the situation where the underlying asset price of the structured product falls to a near knock‐in barrier level. As we have already seen, as the underlying asset price falls, the securities firm, which is put‐long, needs to buy more underlying asset for the hedge.

Recall that the knock‐in barrier is the boundary where the option value either becomes zero or becomes the difference between the strike and the underlying asset price. Put another way, near the knock‐in barrier, the change in δ (called γ) becomes the largest, and as soon as the knock‐in barrier is breached, the underlying asset that has been bought up to that time suddenly needs to be sold.

Of course, in reality, as the underlying asset price approaches the knock‐in barrier, an unlimited amount of underlying asset is not being bought, according to the theoretical δ. If the δ is expected to converge to –1, then appropriate adjustments have already been made before the knock‐in barrier is breached. Even so, we should nevertheless see substantial selling of the underlying asset (or futures) close to the barrier, and indeed what appears to be the impact of this selling has been observed.

This said, occurrences of these observations are few and far between since the underlying asset price needs to fall 30% to 40% or even more before the knock‐in barriers come into place. Probably the most notable occurrences took place in the autumn‐to‐winter period of 2008. This is the period of the global financial crisis, and not only the Nikkei 225 but also single stocks were severely impacted.

While no precise measurements are available, and we can only speak from the observed phenomenon, Nomura Holdings and Daiwa Securities Group, both of which are the giants of the brokerage industry in Japan, may present outstanding examples. Historically, of the two, Nomura boasts a larger market capitalization and generally lower stock price volatility. In pre‐2008 market crashes, almost without exception, the magnitude of the stock price correction was much larger for Daiwa than for Nomura.

During the 2007–2008 global financial crisis, however, the situation flipped. The time series data shows that the magnitude of the price correction in Nomura shares went far beyond that of Daiwa Securities. Perhaps more than a single culprit could be spotted, but one culprit was likely the existence of the structured products. Indeed, in 2008, the number of structured products issued on Nomura Holdings was multifold that of Daiwa Securities.

As the mechanism of hedging dictates, securities firms that took on the Nomura Holdings structured products were put‐long and had to δ hedge their positions by going long on Nomura Holdings shares. When Nomura shares were sold heavily in the market, with the share price coming close to the knock‐in barrier, the firms were forced to sell Nomura shares in significant quantity, which probably contributed to the precipitous fall in the share price.

It is not difficult to imagine that a similar situation was taking place for the Nikkei 225 as well; certainly the precipitous fall in the Nikkei 225 may have triggered the knock‐in puts of the structured products, causing a wholesale selloff of the Nikkei futures by securities firms. We cannot pinpoint the actual impact, unfortunately, as the selloff also undoubtedly came from institutional investors and macro funds trying to hedge their exposure.

That said, when the market is in freefall, what concerns portfolio managers is which stocks will likely be most impacted by the knock‐in structure, if any. Fortunately, structured‐product information is open to the public, and to guesstimate the whereabouts of the knock‐in barriers is not a hard task. Since structured products are aimed at retail investors, the target stocks are generally large‐cap and well‐known names, and since the put structure needs to generate attractive income, the target stocks are also more volatile stocks.

So far, we have seen the potential malaise regarding the underlying asset prices caused by the knock‐in barriers of structured products. Here, a question may arise as to the potential impact of the knock‐out barriers since the knock‐out barriers render options worthless. The quick answer to the question is that the impact is generally small. To understand this, we literally need to further understand the structure of the structured products.

A crucial point is that the barriers of structured products become effective only when the breach of the barriers is monitored and observed. The fact of the matter is that knock‐in barriers are monitored continuously while the monitoring of knock‐out barriers is done only every quarter. This difference in the monitoring process separates the significance of the two barriers.

If the monitoring is done continuously, the change in δ immediately reflects on the underlying asset, which may affect its price, as discussed above. On the other hand, if the monitoring is done every quarter, as is the case for knock‐out barriers, by the time the monitoring date arrives, the change in δ may very well be discounted (i.e., the δ may already be zero).

Of course, if the knock‐out barrier is breached on the day of the monitoring, the δ suddenly becomes zero, leading to a selloff of the underlying asset that has been bought for a hedge. This is a rather rare phenomenon, as we may imagine, and even if it happens, long option holders have likely reduced their positions before the fact, expecting the breach of the barrier, and hence, the impact probably won't be large.

Impact of Convertible Bonds

Convertible bonds (CBs) refer to the bonds accompanied by the right to equity conversion. As the aim of this book is not to make distinctions among convertible bonds, warrant bonds, convertible preferred shares, or sundry other forms of convertible instruments, the discussion here can be understood to apply to these various forms of fixed‐income instruments with a conversion feature. As they stand, the impact these derivative instruments have on the underlying assets is similar, as it derives mainly from the δ hedge mechanism.

As the name implies, CBs are a type of bond issued by corporations to collect funds from investors. Generally, when corporations wish to entice investment money, they issue shares, bonds, or CBs.

If corporations issue shares, their shareholders' equity will increase, but their EPS (earnings per share) will decline, potentially negatively affecting the share price performance. If corporations issue bonds, the number of shares will not increase but debt will. Increased debt means increased leverage, which is not necessarily negative, but larger debt can strangle corporate finance, if the economy worsens or interest rates rise. The corporations may suffer a lower credit rating due to a higher debt‐to‐equity ratio, which also implies more difficulty in organizing new loans.

In the world of corporate finance, CBs figuratively sit between shares and bonds. As they are bonds, the issuance initially and technically does not decrease EPS, even though they generally count as shareholder equity. As stated earlier, however, convertible bonds come in different shapes and forms, and some have forms such that the right of conversion and the bond itself are treated separately for accounting purposes.

While the issuance initially and technically does not decrease EPS, in reality, as soon as the issuance of CBs is announced, the share price gets hammered with few exceptions. The drop in the share price comes from the potential dilution (upon future conversion) of existing shares (called a dilution ratio), and the percentage drop is largely in line with the percentage dilution.

In recent years, since the structure of CBs has increasingly become complex, to decipher the exact impact of dilution, we need to be versed in the prospectus of the issue. For example, a CB called a recap CB is designed so that the convertible is issued simultaneously with share buybacks. In this case, we often see the share price rise upon convertible issuance.

Additionally, for any issuance, if we are able to understand the market sentiment and corporate prospects to some extent, the issuance of CBs may sometimes provide us with an opportunity to buy the shares. Again, this is a generalization, but the share price that drops due to convertible issuance tends to get back on the recovery track by the second or third day after the drop, with the share price often reaching the pre‐drop level within a week.

Let us now turn to the impact of the convertible bond δ hedge. Here again, we cannot ignore the existence of the hedge fund. Convertible bonds are issued by corporations primarily targeting retail investors, but a portion goes to global CB investors and a portion goes to hedge funds commonly known as convertible arbitrage funds.

The δ hedge impact comes from these convertible arbitrage funds. By now, it must be clear that the right of conversion is identical to a call option. The right of conversion comes with a fixed time by which the conversion is allowed (maturity), a conversion price (strike), and its value depends on the volatility of the underlying stock. Convertible arbitrage funds hold the option part of the CBs, and through δ hedge, makes a profit.

Since convertible arbitrage funds are call option long, the hedge should be equity short. If the share price rises, the short position needs to be added (by selling more shares), and if the share price falls, the short position needs to be lessened (by buying back shares). If the share price remains in a narrow range and moves up and down, since the funds are selling shares when the price is up and buying back when the price is down, they naturally end up making a profit.

This simple enough strategy may sound effective without holding option long positions. In theory, it is possible to sell shares outright when the share price goes up and buy them back when the share price goes down. If we repeat this process by using ample funds, we may be able to make a profit as well, but by the same token, we may also see a substantial loss in the process if, for some reason, the share price runs away in either direction.

By holding options long, we can prevent this “runaway” scenario. This prevention mechanism is related to a characteristic of the call option. Recall that by exercising the call option, an investor will receive the underlying asset at strike (conversion) price. For general investors, that is the end of the game. For those that wish to hedge their option holding, as is the case for convertible arbitrage funds, the hedge is done by considering the option's δ, as discussed in the previous section.

For a long call position, the δ of the option increases as the underlying asset price rises relative to strike, and when the underlying asset price goes well beyond strike, the δ converges to 1, corresponding to the probability of exercise reaching 100%. When the underlying asset price falls relative to strike, the δ decreases and eventually becomes 0, meaning the probability of exercise has reached 0%.

If the hedge is done based on the δ, when the share price runs away on the upside, there will be a loss from the short equity position, but since the call option is held long, the loss will largely be cancelled out by the gain on the option's position. When the share price plummets, on the other hand, the equity long position does not exist due to the automatic reduction in the δ, so the loss will be limited to the option premiumpaid.

Incidentally, the largest rate of change in δ generally takes place around the strike, and hence by holding the option, the hedgers not only know how many shares they need to buy or sell but also what share price level will give them the chance to make the maximum profit.

We should also note that positions on single‐stock options do not just come from CBs. Convertible arbitrage funds have call options from CBs, but the same stock may have outstanding options positions created and hedged by brokers. If the strikes of these single‐stock options coincide with those of the options from the CBs, the hedge effect may become even more pronounced.

So far, we have covered the basic information needed to understand the impact of the δ hedge on the underlying equity. When the stocks go up, sell them, and when they go down, buy them back; this process is the process of the δ hedge for option long (γ long in the professional lexicon) positions, and its effect is called the γ effect.

One of the obvious features of the γ effect is to pin down the share price at a certain level (called the pin‐risk), and the “certain level” tends to be around strike (conversion price). The γ also has the characteristic of becoming larger as the option's maturity approaches. As a result, we often see the share price pinned near the conversion price upon maturity of the CB. Our aim in this section is to focus on the δ hedge as a contributing factor to this phenomenon.

This said, the share price being pinned down at the conversion price is not solely due to the γ effect. As noted earlier, if and when CB conversion takes place, a corresponding number of new shares will be issued to the CB holders. Thus, the expected increase in the number of existing shares adds downward pressure on the share price near the conversion price.

Many a time, we have seen the share price jump at maturity of the CB. The phenomenon, in fact, is not limited to maturity, but also witnessed at early redemption. The early redemption clause is often predicated on the share price's remaining above a certain level for a prolonged number of days. The effect of the early redemption clause, therefore, is to keep the share price below such a level.

The above analyses suggest that if we know the conversion conditions of a CB and purchase the underlying shares beforehand, we may benefit from the lifting of the pin‐risk and conversion risk at maturity. Not all shares jump upon conversion or expiry of the CB, of course. With appropriate conditions met, however, we should at least keep in mind that statistics are in our favor.

The number of new shares issued upon conversion of a CB can be calculated by the following equation:

If the δ is 50%, about 50% of the new shares issued are being used for the δ hedge. This estimation, however, is based on the assumption that all of the CBs issued are held by convertible arbitrage funds. In reality, it is safe to assume that a substantial portion of the CB issues are held by retail investors and CB funds.

The question is how to calculate the δ. The exact calculation of the δ is based on the option model and therefore cannot be readily discussed in this literature. If we could access a software that allows us to fathom theoretical option prices, however, the calculation is not all that complicated. As a ballpark measure, the option δ is about 50% at ATM (at‐the‐money).

Since the δ changes according to the underlying asset price levels (in the present case, the share price levels), by calculating the rate of change, the number of shares used for the δ hedge can be estimated. If the number of shares approaches or even exceeds the average daily trading volume of the shares, we can expect significant impact.

To know which stocks are affected by the δ hedge or conversion price can also be guesstimated by observing the share price movement. If the share price appears to be repelled by or pinned to the conversion price, then changes in the share price as it reacts to the expiry or conversion of the CB are large.

The last subject of this section is the δ hedge or the γ effect, when options are held short. When the end‐investors are long option, brokers often face this situation, as discussed earlier, but also, when the CB is equipped with multiple conversion prices, convertible arbitrage funds need to deal with it.

CBs commonly come with a single conversion price, but sometimes we see CBs with multiple conversion prices that are based on the underlying share price levels. Recall that CBs are generally issued by corporations whose intent is to have the CBs converted in the future. The reason for establishing multiple conversion prices, therefore, is to encourage future conversions.

If the new conversion price is to be set higher than the original conversion price, since a higher conversion price entails fewer shares to be issued upon conversion, the holders of the CB will be prompted to convert before the new conversion price goes into effect. Conversely, the new conversion price is typically set lower when the share price performance is poor. The lower conversion price will give CB investors, who could not convert at the original conversion price, the chance to convert at the new conversion price.

Obviously, the conversion price cannot be indefinitely reset to lower levels. If the conversion price is reset too low, an enormous number of shares will be issued upon conversion, which drives the share price even lower. Accordingly, the reset of the conversion price usually comes with a lower limit, the limit commonly accompanied by the mandatory conversion clause.

The mandatory conversion clause literally requires conversion to take place at some given time. What will happen if the share price keeps on going down beyond the mandatory conversion price? For CB investors, this is akin to holding a put option short.

Investors who are short put, for example, if the strike is at JPY100 and the share price is at JPY50, need to buy the JPY50 shares at JPY100. A way to avoid the potential loss incurred is to hedge the short‐put position, and the hedge will be the opposite of that for a long option position (i.e., stocks are sold when the share price goes down and stocks are bought when the share price goes up). Clearly, the process generally increases volatility.

The manifestation of this process became most prominent in Japan during the financial crisis of 1998. Many Japanese banks, in order to strengthen their financial base, had issued a large number of convertible preferred shares with the mandatory conversion clause.

As nonperforming loans of the Japanese banks came into focus again due to the crisis, the bank share prices took a hit. Convertible arbitrage funds, which held a significant portion of the convertible preferred shares, had probably never thought that the share price would drop to the levels where the mandatory conversion would be triggered.

As the long‐call positions turned into short‐puts, the funds were forced to sell shares for a δ hedge. The selling that invited more selling came to be known as the “death spiral,” and the world came to realize the danger of option short hedge perhaps for the first time in history.

Inverse and Leveraged ETFs

We just saw the γ effect of the option short position potentially contributing to the increase in single stock or market volatility. Something similar to the option γ effect can actually take place outside options.

In recent years, financial instruments called ETFs have enlarged their presence in the market. ETFs stand for Exchange Traded Funds and denote funds traded in the exchange as though they are equities. There are many kinds of ETFs, but in view of their impact on the market, inverse and leveraged ETFs particularly deserve a mention.

Inverse ETFs are the ETFs whose price moves in the opposite direction to the price of the underlying asset of the ETFs. For example, the price of the Nikkei 225 inverse ETF falls 10% when the Nikkei 225 rises by 10%. Leveraged ETFs, on the other hand, move in the same direction with the underlying asset but with a leverage. For example, when the Nikkei 225 rises by 10%, the Nikkei 225 2x leveraged ETF will rise by 20%. In these cases, the question is what the ETF managers do.

When the Nikkei 225 rises by 10%, the holder of the 2x leveraged Nikkei 225 expects his or her asset value to rise by 20%. In other words, the manager of the ETF must purchase 20% of the asset linked to the Nikkei 225. Conversely, if the Nikkei 225 falls by 10%, the manager needs to sell 20% of the asset linked to the index.

The process of “buying when the underlying asset price goes up and selling when it goes down” is indeed similar to the process of the option‐short δ hedge, potentially leading to the γ effect. In addition, as with the case of the δ hedge, since the asset value is settled after the market close, the selling or buying becomes concentrated near the close.

For the Nikkei 225 and TOPIX inverse and leveraged ETFs, the underlying assets traded are the futures. Compared with the total trading volume of Nikkei 225 and TOPIX, the ETF‐related futures volumes are limited in quantity. Since the ETF‐related trading is all done in the short period of time near the close, however, the impact becomes more exaggerated.

A “hedge” required for inverse ETFs is similar to that for leveraged ETFs (1x inverse hedge corresponds to 2x leveraged hedge). Let us assume that the size of the asset under management is 100. If the ETF is the 1x inverse index ETF, then the futures used for this structure are a negative 100 (short 100 futures). If the index rises by 10%, then the index will be 110, and the futures value will be a negative 110. The asset under management is now 90, so the futures needed for the “hedge” will be negative 90, so the asset manager needs to buy back 20 futures.

If the γ refers to the needed adjustment in the asset under management relative to a 1% move in the size of the underlying asset, then the leveraged and inverse ETF γ can be calculated by the following equation:

For inverse ETFs, 1x inverse corresponds to 2x leverage, and 2x inverse corresponds to 3x leverage, so these numbers should be substituted in the above equation to calculate the appropriate γ.

The list of Nikkei 225 and TOPIX ETFs is publicly available. As of September 2015, the largest ETF was the Nikkei 225 2x leveraged ETF (Security code: 1570) set up and managed by Nomura Asset Management. Since the ETF offered 2x the return of the Nikkei index, the popularity of this ETF skyrocketed, with its trading volume surpassing that of the Toyota stock, amounting to some 14% of the total equity trading volume in the Tokyo Stock Exchange.

The collapse of the Chinese equity market, which began in August 2015, generated a reversal of fortune for this ETF, however. The manager was forced to sell Nikkei futures, which in turn, added downward pressure on the Japanese equity market. Since that time, whenever the equity market goes up and down in a significant way, professional traders tend to focus on index inverse and leveraged ETFs.

Put/Call Ratio

Market participants often speak of the put/call ratio. The ratio, calculated by dividing the 5‐day average trading volume of the exchange‐traded put options by the same 5‐day average of the call options, is commonly viewed as a measure of the market sentiment. If the put trading volume is larger than that of the call, option investors are believed to be more pessimistic about the market, and vice versa.

The trend in the exchange is likely mirrored in the over‐the‐counter market. As stated earlier, over‐the‐counter trades are hedged by brokers more often than not, and therefore, an augmentation of put‐long positions implies the augmentation of the short‐put γ effect, and an augmentation of call‐long positions implies the same of the short‐call γ effect. Needless to say, the impact depends on the size of the positions, but at least in theory, a rising put/call ratio suggests a rise in the downside market risk, and a falling put/call ratio suggests a rise in the upside market risk.

If this is the case, wisdom seems to dictate that we should be selling the Nikkei 225 futures whenever the Nikkei put/call ratio rises and buying the Nikkei 225 futures whenever the put/call ratio falls. As usual, the reality is not that simple. In fact, our experience tells us to do the opposite. This is a phenomenon akin to “buy on the dip,” which means that the market is more likely to rebound after a big drop.

More concretely, let us look at the cases where the Nikkei put/call ratio jumped in the last 10 years. If we take the top 30 largest jumps, 53.3% of the time, the Nikkei 225 recorded a gain a week after. So, the result is about 50/50. Two weeks afterward, however, the number rises to 63.3%; a month after, 72.4%; and two months and three months after, 64.3%. In other words, at least probability tells us that a jump in the put/call ratio offers a good buying opportunity.

Once again, the key word is “probability.” The gain recorded 64.3% of the time means that the returns are negative 35.7% of the time, which is a loss ratio of 1 out of 3, and the number may not be easily brushed off. What is important is to judge under what circumstances the put/call ratio has jumped and what caused the jump. It goes without saying that the judgment hinges on various factors, such as the macro environment, policy announcements, or other events.

The put/call ratio also has a close relation to the option skew. The option skew is the shape of the implied volatility curve, expressed simply, the spread between the implied volatility of the call option and the implied volatility of the put option. The spread is calculated by subtracting call option implied volatility above the strike (usually 5% to 10% above) from the put option implied volatility below the strike (usually 5% to 10% below), and is expressed as a percentage.

Stated another way, while the put/call ratio expresses the ratio of the traded volume, the skew expresses the difference between the put and call implied volatility. If the skew is large, puts are being bought more aggressively, which suggests increased concern on the downside, and if the skew is small, the contrary may be true. It is difficult to say which skew levels offer a clear buy or sell signal on the equity market. The skew simply reveals the views of option investors and probably depends on the market conditions of the time.

VIX Index

When we speak of volatility, we cannot avoid discussing the VIX Index (the “fear index”). The VIX Index was developed by the CBOE (Chicago Board Options Exchange) to measure the future volatility of the S&P 500 and is calculated from the volatility attained from the collection of S&P 500 option prices.

The actual formula is complicated and replicating it in this literature offers no merit, but we can think of it as the volatility calculated from 30‐day S&P 500 options with various strikes. In other words, the VIX Index expresses the implied volatility of the broad market (i.e., expected near‐future volatility of the S&P 500).

If this index is high, at least option traders are expecting the future market volatility to be high, and vice versa. The higher the expected future volatility, the higher the expected rate of future market fluctuation, and as discussed earlier, since the market tends to display higher volatility when it goes down, the name “fear index” was coined. With this premise, can we say that the equity market is a “sell” when the VIX Index spikes up? The answer, again, is “not necessarily.”

In September 2008, Lehman Brothers filed for Chapter 11, ending its long corporate history and, at the same time, inadvertently becoming the symbol of the global financial crisis. The VIX Index was accused at the time of failing to “foresee” this significant event.

As elaborated in the “Historical and Implied” section above, we seldom see implied volatility rise before historical does. In other words, implied volatility spikes only after the market plummets. What this fact suggests is that when the implied volatility jumps, it is often “too late.” This is not hard to understand, since if option traders could foresee the market collapse before it takes place, they might as well trade their own funds rather than working for brokers or hedge funds.

Indeed, we see many occasions where the market rebounds after a sharp rise in volatility, implying that had we sold the market (via selling index futures) after the VIX Index spikes, we could have suffered a substantial loss. If this is the case, then, should we hold on to the market in the face of sharp jumps in the VIX Index? The answer, obviously, depends on how long we should hold on to the market and which stocks we should retain.

The collapse of Lehman Brothers in September 2008 and events that took place in the following days took the VIX Index to a new high, and the tumultuous market saw no end until March of 2009. Still, this is nothing but an afterthought. The fact of the matter is that no one knew at the time that the global financial crisis would end (in a way, it did not, as the subsequent Euro crises suggest). Probably it would have been best not to own any stocks during those times, and if we had to own stocks, we should have just stuck to defensive stocks such as those in the food, pharmaceutical, railway, and utility sectors.

Where the above discussion leads is that we should probably not automatically turn buyers of the market after a sharp rise in the VIX Index, and the converse is also probably true. What we may say, however, is that low volatility generally means market complacency and low inter‐stock correlations and, thus, does not last indefinitely.

Also, as stated in the “Volatility” section above, volatility tends to mean‐revert and hence never becomes zero as long as the market is alive. In other words, if the volatility is falling in an up market, the market will necessarily go down, and in the down market, the market will necessarily go up. Forecasting the exact timing of rebounds or downturns is not easy, but by looking at the market as a whole (economy, FX, and interest rates, for example), we can guesstimate which way the market is headed and prepare for the upcoming changes.

As alluded to in the “GPIF” section in Chapter 2, we have seen occurrences of global shifts of funds triggered by the spikes in the VIX Index. It is not surprising to see active portfolio managers taking actions based upon the levels of the VIX Index. Nor is it surprising to see program trading that includes the VIX Index or some other measures of market risk in its algorithm.

If the majority of the market participants are utilizing the same or similar measures or rules, the market will move by them. The likelihood of one of the measures being the VIX Index or another measure of volatility is quite high, and therefore when the VIX Index spikes up, shifting to defensive stocks, such as high‐dividend‐yield stocks, might be wise.

We may note, however, that in judging when to move back to growth or value stocks from defensive ones, neither the VIX nor other measures of volatility are very useful. When the VIX Index spikes up, chances are that it will come down in a matter of days, but we may not want to abandon our defensive posture.

The VIX Index spikes up for a reason, and even when it comes down, often the “reason” still exists. The history of the VIX Index or other market volatility indices tells us that spikes tend to occur in a cluster. When, then, can we turn from defense to offense? The discussion is left to the next chapter.