Chapter 21

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Managing Your Portfolio

Putting it all together

‘There is a difference between knowing the path and walking the path.’

Morpheus

Top-down you have allocated your assets and, from the bottom up, you have selected the underlying investments for your portfolio. Now you need to marry these two opposite perspectives together into a coherent portfolio.

Portfolio construction does that. It involves deciding how much to allocate to each underlying investment, ensuring your portfolio is efficiently aligned with your investment strategy.

In this chapter we review portfolio construction and implementation. We cover the steps to transfer your investment strategy and fund selection from a theoretical exercise into an actual portfolio and its ongoing maintenance.

Three budgets

When managing your portfolio consider three budgets and how much to spend on each:

1. Risk budget.
2. Fee budget.
3. Governance budget.

Your decision impacts your investment outcome and the amount of time and money you will spend managing your portfolio.

Risk budget

Risk budget is your portfolio’s maximum risk level. It is a function of your risk tolerance, dynamic investment strategy and market conditions.

Absolute risk derives a portfolio’s absolute return. The risk level should match your risk tolerance and the required return for achieving your objectives. As your risk tolerance and investment strategy change throughout the phases of your life cycle, so does your portfolio’s absolute risk level.

Absolute risk is also a function of market conditions. When you are concerned that markets are fragile, reduce it. When believing markets will rise, increase it.

Relative risk refers to deviations between returns of funds and their passive benchmarks. On a portfolio’s aggregated level, relative risk measures the deviations between portfolio returns and SAA.

From the SAA, construct a composite benchmark. It blends indices representing each asset class with SAA weights. For example, the composite benchmark of a 60% UK equity and 40% bond SAA could be 60% FTSE 100 Index and 40% FTSE Actuaries UK Conventional Gilts All Stocks Index.

Your portfolio’s performance is expected to deviate from that of SAA because of active asset allocation, security selection, costs and other discrepancies between a theoretical SAA and actual portfolio.

Control relative risk through magnitude of active asset allocation positions and fund selection. Larger deviations between SAA weights and those in your portfolio increase relative risk. Using more active funds, each with a relative risk with respect of its benchmark, also increases relative risk. Minimising deviations between SAA weights and active asset allocation and using more index trackers instead of active funds reduce your portfolio’s relative risk.

Strike a balance between keeping close to your SAA and investment strategy, from one side, and aiming to add alpha through active asset allocation and security selection, from the other side. Deviating too much, you can end up with a mismatch between your portfolio and investment strategy. Not deviating, you can miss alpha opportunities.

Fee budget

Fee budget is how much money you are spending on your portfolio. Normally, you pay a fixed fee to your pension and ISA providers. Investments have different price tags based on their type.

Active funds are more expensive, but they can add excess return above benchmark. However, active funds can also underperform. Trackers are cheaper, but they add no alpha and market-cap indices can have some deficiencies.

Set your fee budget based on your platform’s investment choices (availability of attractive funds may warrant a higher fee), your conviction in active funds’ potential alpha and your required net of fee returns.

For example, assume your investment strategy is 50% equity and 50% bonds. Your equity expected return is 8% and that of bonds is 2%. This expected return is for asset classes, not considering costs and alpha. Your portfolio’s gross expected return is 5%.¹

Say you can choose:

1. Active equity fund with 2% target alpha net of fees and 1% OCF.
2. Equity tracker with 0.50% OCF.
3. Active bond fund with 1% target alpha net of fees and 0.50% OCF.
4. Bond tracker with 0.20% OCF.

If you have a high conviction that the active funds are likely to meet their return objectives, paying extra fees is worthwhile. The potential alpha is 1.5% for a 0.75% OCF.² Anyway, you must pay a 0.35% OCF for trackers, so you pay an incremental 0.40% for a potential 1.5% alpha.³

If you lack conviction in the ability of the funds to meet their target returns and you are concerned that alpha might be negative, go with trackers, paying 0.35% OCF.

If you do not want to spend more than 0.60% on fees, select your higher-conviction active fund and one tracker.

Governance budget

Time is money. Time is one of our scarcest resources. Governance budget is the amount of time you spend governing your portfolio. You may enjoy investing – spending your leisure time with your portfolio could be a pleasure. However, most people want to spend as little time as possible with their pension, in particular because you cannot use the money until retirement.

To minimise your governance budget, keep it as simple as possible. Leonardo da Vinci said that, ‘Simplicity is the ultimate sophistication.’ Simplicity does not necessarily mean you settle for a lower quality.

An extremely simple portfolio includes a single holding of a global or UK equity tracker. This ‘buy and forget’ investment strategy requires minimal monitoring. However, it is not for the faint-hearted. It is volatile and lacks an active manager overlooking risks.

Buy-and-hold strategy involves formulating an asset allocation, buying investments and holding them statically. It needs planning and setting up at the onset. However, once the portfolio is in place, it is low maintenance. It requires a review every couple of years and when you switch phases in your life cycle, but not much more. It is light on governance.

Some savers dynamically change their asset allocation and often switch active funds. Such strategy is demanding on governance.

However, dynamic management is not always profitable. Changing your portfolio generates transaction costs and bad investment decisions can hurt performance.

The more sophisticated and opaque your portfolio, the more governance is needed. Unless you blindly trust fund managers to do a good job for you, monitor your investments. Saving for your financial future is too important to leave unmonitored.

Simple, governance-light, buy-and-hold strategies are appropriate for you if you are not actively managing your portfolio. Dynamic, governance-heavy strategies are appropriate if you are actively managing your portfolio.

Portfolio construction

We are looking to construct a portfolio as simply as possible. The objective is to minimise the demand on the three budgets of risk, fees and governance. One efficient portfolio construction methodology is core-satellite.

Core-satellite

A core-satellite divides your portfolio into core and satellite – no surprises there. The core is around 50% to 80% of the portfolio (depending on how much alpha you seek from active management), made of trackers aligned with the asset classes in your SAA. Some assets can be accessed only through active management even when they are part of the core, such as direct property.

For example, your SAA is 50% equity, 40% bonds and 10% cash. For the core you allocate 40% to equity trackers, 32% to bond trackers and 10% to cash.⁴ Cash does not follow a core-satellite approach.

The core’s relative risk is low since tracking error with the SAA composite benchmark is minimal. Fees of trackers are relatively cheap. The demand on governance is light, because you do not select and monitor active funds or sophisticated investments. The core has modest demands on the three budgets.

As for the satellite (10% equity and 8% bonds), make it punchy. Use high-­conviction active funds, aiming to add alpha. These funds are riskier than trackers, more expensive and require selection and monitoring. They are demanding on the three budgets. However, they make less than 20% of the overall portfolio so risk, fees and governance are under control.

Implementation

The objectives of implementation are aligning as closely and efficiently as possible your actual portfolio with your target portfolio, minimising tracking error and transaction costs. The portfolio should reflect your target asset allocation (SAA and active allocation), as well as size allocations to your chosen funds.

A SIPP is the most flexible pension for implementation. It offers the widest selection of investments. However, since the menu on some DC platforms is limited, use your stocks and shares ISA to complement it. The choice of funds and ETFs in your ISA can be wider than that in your pension.

ETFs

When implementing TAA views, ETFs offer a number of advantages compared with actively managed funds. Typically, TAA expresses short-term views. Therefore, ETFs minimise transaction costs of buying and then selling funds. Trading ETFs is normally cheaper than trading active funds, since ETFs are more liquid.

When investing in active funds, plan to hold them for the long term, allowing fund managers sufficient time to generate alpha. Using active funds for TAA purposes does not make sense.

Constructing a portfolio

Table 21.1 shows an example of portfolio construction. The portfolio spans a pension and ISAs, it is divided between core and satellite and TAA is implemented using ETFs.

Your actual portfolio will not perfectly match your target portfolio. There are constraints, such as the amounts you can hold in your pension and ISAs, the choice of investments, minimum investment amounts and timing of cash flows. The best you can do is try to keep it as aligned as possible. It will not be perfect.

The number of active funds for each asset class depends on its allocation’s size and styles of funds. Large allocation warrants manager and style diversification. If active UK equities are 20% of your portfolio, for example, consider splitting the allocation amongst two or three managers, ideally with complementary styles.

Table 21.1 Implementation

	Allocation %	Selection %	Implementation
Global equities	18	15	Core, tracker, in pension
		3	Satellite, active fund, in pension
European equities	5	5	TAA, ETF, in ISA
Emerging market equity	2	2	Core, tracker, in pension
Emerging Asia	5	5	TAA, ETF, in ISA
Total equity	30	30
Gilts	28	22	Core, tracker, in pension
		6	Satellite, active fund, in pension
IG credit	12	10	Core, tracker, in pension
		2	Satellite, active fund, in pension
Global high yield	5	3	Active fund, in pension
		2	TAA, ETF, in ISA
EMD	5	3	Active fund, in pension
		2	TAA, ETF, in ISA
Total bonds	50	50
Cash	5	5	Cash ISA
Property	10	5	Core, active fund, in pension
		5	TAA, active fund, in ISA
REITs	2.5	2.5	Core, tracker, in pension
Commodities	2.5	2.5	Core, tracker, in pension
Total alternatives	15	15
Total	100	100

Complementary styles mean investment approaches with different characteristics that should perform differently during different market conditions. For example: value/growth (50% value, 50% growth), large/SMID (small and mid) cap (80% large, 20% SMID) and aggressive/defensive.

Rotate the style allocation based on your views. For example, overweight value and SMID cap, as they tend to outperform growth and large cap over a full economic cycle. Split aggressive and defensive based on market conditions.

If the allocation to an asset class is low (such as up to 5%), use a single, high-conviction core manager. Core managers usually do not have a bias to any particular investment style, such as neither value nor growth.

Trade orders

When trading funds and financial instruments, you can use several types of orders. Market order instructs the broker to buy or sell at the best currently available price. Limit order is conditional. It is used to buy or sell at a specific price or better. Use market order when you want to fill the order at whatever price. Use limit order when price is more important than filling the order.

Stop loss order is triggered only when a specified price has been reached. Use it to limit the downside of positions (or to take profits) by automatically selling them at a predetermined price. The downside is that if price drops and then recovers you might miss the rebound.

Derivatives

Derivatives are not financial weapons of mass destruction. They might be notorious since they have been involved in some financial scandals, but it is not the derivatives’ fault, but that of those who abuse them.⁵

Derivatives are a helpful financial tool, instrumental in efficiently managing portfolios. They are not for everyone. You need an intermediate or advanced knowledge in investments and portfolio management to use them.

The two fundamental derivatives are forward contracts (futures in their standardised form) and options. By combining them, sophisticated, complicated derivatives are created, often called exotic. However, our focus is on standard plain vanilla listed futures and options on indices.

Futures

Futures contract is an agreement between two parties to buy or sell an asset (underlying) for a price agreed today (futures price) but with payment and delivery at a future date (delivery date or contract maturity). Underlying assets include stocks, bonds, commodities and currencies. Maturities are often one or three months.⁶

Forward contracts were originally developed for hedging. For example, you are a farmer growing wheat. The harvest is next year. You can either wait until the harvest to sell the wheat at whatever the prevailing price or sell a forward contract obliging you to sell it next year for an agreed fixed price. With the forward, you lock in a price. If the wheat price falls, you do not lose. However, if the price jumps, you do not benefit. You hedged it. A farmer should focus on growing wheat, not gambling on its price.

Futures contracts are standardised forward contracts, traded on an exchange. When buying (going long) or selling (going short) a futures contract, each contract is written on a defined number of the underlying’s units.

For example, you want to go long the FTSE 100 Index.⁷ The futures contract written on the index has a £10 multiplier (unit of trading), meaning each contract is for £10 of the underlying index price (index point). The current FTSE 100 Index’s price is 6,500.

The futures economic n × m × p.

Where n is the number of futures contracts, m is the multiplier and p is the underlying asset’s price (spot price). In this case, each futures contract gives an exposure of £65,000 to the FTSE 100 Index.⁸

Futures are unfunded, meaning when buying or selling futures, you do not need to commit all the exposure. Rather, you deposit a margin with the exchange to mitigate counterparty risk.⁹ The futures contract is marked-to-market daily. You add money to the margin when the futures position loses and receive money back when it gains.

In this example, the initial margin is 25%. You deposit £16,250.¹⁰ Effectively, it is a synthetic leveraged position on the FTSE 100 Index – investing £16,250 to get a £65,000 exposure. If, the next day, the index falls 1%, you add £650 to the margin facility. If the index gains 1%, you receive back £650. The futures price moves almost in the same way as the spot price (without optionality, called delta one).

Futures price converges with the spot price as the contract approaches its expiry date. When the contract is close to expiry, you can either let it expire and cash settle it or roll it over to the next futures contract (closing or winding down the existing futures and buying a new one with a later maturity).¹¹

When the futures curve is downward sloping (backwardation), the closer futures price is higher than next futures price. Rolling costs are positive – you close more expensive futures than the one you roll into. When the futures curve is upward sloping (contango), the closer futures price is lower than the next futures price. Rolling costs are negative – you close cheaper futures than the one you roll into.

Over recent years, futures trading and rolling costs have increased.¹² The annualised rolling costs of some futures on equity indices have soared from single digit basis points to 30 to 50 basis points. It is often cheaper to use ETFs. Whilst ETFs charge a TER and they are funded, they have no rolling costs.

Whether to use futures or ETFs depends on your holding period. Futures may be better for a short time (small number of rolls), whilst ETFs may be better for a longer time.

The advantages of futures are that it is easy to short them and they are liquid, unfunded and cost efficient. Also, since profit and loss are based on the underlying’s price changes in local currency, your position has no currency exposure (although most futures are based on price return, not total return, so they returns exclude dividends).¹³

Options

Options give the right but not the obligation to buy (call option) or sell (put option) an asset for an agreed price (strike price) at (European option) or before (American option) a maturity date.

When buying an option, you pay a premium. If, at maturity, the option is ‘in the money’ your profit is the option’s payoff minus the premium.^14,15 If, at maturity, the option is ‘out of the money’, it expires worthless, and you lose the premium.

The basic uses for options are bullish long call and bearish (protective) long put.

For example, the FTSE 100 Index is at a level of 6,500. You think it may rally above 7,000, but you are unsure and concerned it might fall. You buy a one-month call option on the FTSE 100 Index with a strike of 7,000 for a £200 premium.

If, indeed, the index rallies to 7,300, your payoff is £300 and your profit is £100.¹⁶ If the index ends at a level of 6,900 after a month, your option expires worthless, and you lose the premium (your downside is limited to the premium).

Once again, the FTSE 100 Index is at 6,500. You hold equities in your portfolio and you are concerned the index might crash. You buy a one-month put option with a strike of 6,000 for £200. If the index falls to 5,500, your payoff is £500 and your profit is £300.¹⁷ You insured some of your portfolio’s downside.

The advantages of options are optionality, risking only the premium, leveraging your position by spending only the premium and going long volatility (option price depends on volatility so, when volatility rises, the option price rises as well).¹⁸ The disadvantage is if an option expires worthless you can lose your entire premium.

This was only a high-level taste of derivatives.

Currency management

Global investing includes exposure to fluctuations in exchange rates between your home currency and foreign currencies. They can have a huge impact on returns measured in your base currency.

For example, you invest in an S&P 500 Index tracker. The index rises 10%. However, the British pound appreciates by 5% versus the US dollar. When translating the return from US dollars to pounds, it is about 5%, instead of 10%.¹⁹

Over the long term, currencies tend to oscillate around a certain level. When holding foreign investments for a long run, currency impact could wash out. However, currency movements can notably impact returns over the short and medium term.

When investing in equities or other risk assets, consider three options:

1. Keeping the foreign currency exposure.
2. Buying funds’ hedged share classes.
3. Hedging the currency exposure.

Whether hedging the currency or not, foreign equity investments are volatile. Therefore, you can keep the currency exposure, bearing in mind that you will experience times of disappointing performance when your base currency appreciates. A strong British pound is good when you travel abroad – everything is cheaper. However, it is bad for your un-hedged foreign investments.

The second option is buying funds’ currency-hedged share classes. Pay careful attention to whether the share is measured in pound or hedged to pound.

A share denominated in pound means returns are translated into pound. However, you are exposed to the foreign currencies of the fund’s assets. A hedged share means the currency exposure of the fund’s assets is hedged to the share class’ currency, mitigating currency risk.

A perfect hedging means your return equals the return in local currency. In the example of the S&P 500 Index tracker moving up 10% and the pound appreciating 5%, a perfectly hedged return is 10%. The effects of currency fluctuations are removed.

However, in the real world, hedging is not perfect. There are transaction costs and the hedging ratio is not 100%.²⁰

One cost or benefit of hedging is differences in short-term interest rates between the home and foreign currencies. For example, if the US dollar short-term rate is 0.5% and that on the British pound is 1%, hedging US dollar back to pound generates a return of 0.5%.

Hedging the dollar is like borrowing in dollars and lending in pounds. Effectively, you offset your long US dollar position with a short position (borrowing in dollars), paying a 0.5% interest rate. You offset your short dollar position with a long position (lending in pounds), collecting a 1% interest rate.

The third option to hedge currency is doing it yourself. You can use derivatives, such as currency forward or futures contracts. This may be unavailable in your pension or ISAs. Another way is borrowing and lending in the respective currencies to offset your currency exposures. But this could be complex to implement and time-consuming to monitor.

When investing in emerging market assets, the cost of hedging might be high and it might be overly complicated, due to a large number of currencies. When investing in emerging market equity and emerging market debt (EMD), accepting currency risk may be a necessity. EMD in hard currency can be easily hedged.

Choosing between hedging and not hedging risk assets should depend on your view on currencies. Thinking your base currency is likely to appreciate, hedge some or all of the foreign currency (all if your conviction is high, half if it is not high). If you think your base currency is likely to depreciate, do not hedge.

When investing in bonds or conservative assets, the rule of thumb is to always hedge their currency exposure. Conservative assets’ volatility can more than double with currency risk. The asset can lose its intended role in your portfolio, turning from a conservative to a risk asset. If you are unable to hedge the currency risk, you should probably not invest in foreign conservative assets.

Currency valuation

How could you form a view on currencies?

Evaluating currencies is difficult. Exchange rates should be set by fundamentals (carry, valuation). However, in practice, sentiment and trading patterns (momentum) drive currencies’ prices.

Purchasing Power Parity (PPP) is an economic model used to determine currencies’ relative values. According to PPP, in the long run, a basket of identical goods and services should cost the same across countries (law of one price). Therefore, exchange rates should move to a rate equalising this basket’s price.²¹

For example, according to the Big Mac Index, a McDonald’s Big Mac should cost the same in London and New York City.²² If it costs £2.89 in London and $4.79 in NYC, it implies an exchange rate of 1.66 £/$ (one British pound equals 1.66 US dollars).²³

In practice, goods and services have different prices across countries because of differences in quality, barriers to trade and departures from free competition. Yet, PPP should provide a fair-value, long-term yardstick for currencies.

Another economic model used to estimate future exchange rates is Covered Interest Rate Parity (CIRP). CIRP claims that interest rate differential between two currencies equals the differential between the future exchange rate and spot exchange rate.

(1 + r_£ = (1 + r_f) F ÷ S

Where r_£ is interest rate of local currency, r_f is interest rate of foreign currency, S is spot exchange rate and F is future exchange rate.

For example, say the interest rate of the British pound is 0.50%, that of the US dollar is 0.25% and the spot exchange rate is 1.55. According to CIRP, the future exchange rate is 1.554.²⁴ This means a currency with a higher interest rate is expected to appreciate versus one with a lower rate (more dollars are needed to buy each pound).

Empirical evidence supports CIRP. Investors are attracted to currencies with higher rates, creating demand and pushing their price upwards. However, like other financial theories, exchange rates can deviate from levels that CIRP and PPP predict for long time periods; sometimes years.

Trading currencies involves costs. Even when your bank does not charge a dealing commission, costs can be embedded in the bid-ask spread. Carefully check the quoted exchange rates for buying and selling currencies.

Rebalancing

Portfolio rebalancing is realigning the portfolio’s weights with the target asset allocation weights. Different assets perform differently. Over time, weights of strongly performing assets increase, whilst those of lagging assets decrease.

Once in a while – every 3, 6 or 12 months, depending on asset movements – realign the portfolio by selling strongly performing assets and buying weakly performing ones. Alternatively, instead of selling assets, generating transaction costs, use cash inflows to buy only lagging assets, increasing their relative weights. After retirement, use cash outflows to reduce weights of strongly performing assets.

This ensures the portfolio’s asset allocation matches your investment strategy. Otherwise, you might end up with a portfolio drifted from the risk and return profile matching your objectives.

For example, you start with a 50% equity and 50% bond portfolio. In a year, equities returned 18% whilst bonds fell 4%. Your portfolio now has 55% in equities and 45% in bonds.²⁵ Its risk level is higher than intended, due to higher allocation to equities. Selling 5% equities and buying 5% bonds aligns the portfolio with its 50/50 target allocation.

Rebalancing introduces a healthy discipline of taking profits on winners and buying cheap recent losers. However, use discretion. If you believe bonds are likely to continue dropping, for instance, consider keeping the weights as they are or selling equities and buying cash instead of bonds.

Asset allocation should be adaptive to your current market views when rebalancing your portfolio.

Cash flow management

During the accumulation phase, cash flow management for pension investing normally means you have a standing order to allocate monthly contributions across your choice of funds. Investing on a monthly basis leads to a dollar-cost averaging, avoiding buying at market’s peak. Instead, you buy your investments at an average monthly price.

Invest cash quickly; otherwise your portfolio can suffer a cash drag. Uninvested cash does not participate in markets, lacking upside or downside. When markets rise, cash drags performance down. When markets fall, cash can help performance. However, before celebrating, it is not a deliberate allocation to cash so it should be avoided unless intended. This is especially relevant when topping up your pension or adding lump sums to ISAs.

During the de-accumulation phase, the direction of cash flows reverses. Cash flow management should focus on minimising taxes and costs.

Normally, you can take a tax-free lump sum of 25% of your pension upon retirement. Following that, you may have to pay income tax on pension drawdowns.

You can take out as much as you want when you want. But spread it over separate tax years to minimise income tax. For example, if every year you take only £10,000, it is tax free within your personal allowance.

Use cash outflows to gradually change your portfolio’s strategy. If, for example, you wish to de-risk your portfolio over time, sell more risk assets than conservative assets when raising cash. As your time horizon shrinks, you can gradually increase your portfolio’s liquidity by selling some illiquid assets every time cash is raised to generate a cash outflow.

If you live for a couple of years from the tax-free lump sum, or have other sources to finance your living, consider taking about £10,000 tax-free each year out of your pension, adding it to your ISA. Then, after accumulating money in your ISA for a number of years, draw the money without paying income tax.

Drawing capital in volatile markets requires a plan. Limit withdrawals and mini­mise income, aiming to delay drawing capital at depressed prices. Try drawing investment income instead of capital. Build up a cash buffer, trying to hold one or two years’ income, allowing you to sit tight and wait for a recovery.

Summary

• When managing your portfolio, consider the risk, fee and governance budgets.
• A core-satellite portfolio construction considers the three budgets. The core is aligned with SAA (minimising risk), consisting of mainly trackers (minimising fees) and keeping it simple (minimising governance). The satellite aims to add alpha.
• Implementation is translating your investment strategy and fund choices into an actual portfolio. Use ETFs for efficiently implementing short-term views. Use stocks and shares ISAs to complement your pension, if needed.
• Currency fluctuations can have a big impact on results. Either hedge or do not hedge currency of risk assets. Always hedge currency of conservative assets. Buying funds’ hedged share classes is the easiest way to hedge currency. Ensure the share class is hedged, not just denominated in British pound.
• Rebalancing is realigning your portfolio with its target weights to correct drifting weights, due to market movements. Use cash flows to rebalance to reduce transaction costs. Rebalance to an allocation adapted to current market views.
• Cash inflows into your pension are normally invested on a monthly basis across your choice of funds. This is dollar-cost averaging. When retiring, spread drawdowns to minimise income tax.

Notes

¹ 5% = 50% × 8% + 50% × 2%.

² 1.5% = 50% × 2% + 50% × 1%; 0.75% = 50% × 1% + 50% × 0.50%.

³ 0.35% = 50% × 0.50% + 50% × 0.20%.

⁴ 40% = 80% × 50%; 32% = 80% × 40%.

⁵ The main risks of derivatives are basis risk (the derivative’s return differs from that of the underlying), counterparty risk (for OTC derivatives), complexity, leverage and short selling.

⁶ Most contracts expire in less than a year. A number of contracts last longer, sometimes more than two years. Many contracts expire quarterly – in March, June, September and December.

⁷ Go online to check the factsheet of a futures contract or the website of the exchange for details.

⁸ If you want an exposure of £100,000 to the FTSE 100 Index, either choose one contract for an exposure of £65,000 or two contracts for an exposure of £130,000. You cannot get precisely £100,000.

⁹ One advantage of futures over forward contracts is that your counterparty is the exchange, effectively eliminating counterparty risk.

¹⁰ £16,250 = 25% × £65,000.

¹¹ Cash settlement is settling the futures contract by cash rather than by physical delivery of the underlying asset.

¹² The roll yield is the yield holders of futures capture when a futures contract converges with the spot price. It is positive when the futures curve is in backwardation and negative when the curve is in contango.

¹³ A contract for differences (CFD) is a derivative agreement between a buyer and seller, whereby the seller pays the buyer the difference between the current price of an asset and its price in the future. If the difference is negative, the buyer pays the difference to the seller.

¹⁴ The strike price is above spot price for a call option or the strike price is below the spot price for a put option.

¹⁵ Payoff of a call option is strike price (X) minus spot price (S). Payoff of a put option is spot price minus strike price. C = Max (0,X − S) and P = Max (0,S −X). Where C and P are payoffs of call (C) and put (P) options.

¹⁶ £300 = £7,300 − £7,000; £100 = £300 − £200.

¹⁷ £5,00 = £6,000 − £5,500; £300 = £500 − £200.

¹⁸ Some option strategies risk more than the premium, such a naked put or call writing (selling). Uncovered put or call is selling options without shorting or holding the underlying for coverage.

¹⁹ More precisely, the return is 4.76% = (1 + 10%) ÷ (1 + 5%) − 1.

²⁰ Hedging ratio is the ratio between the market values of the hedging instruments and hedged assets. For example, when holding $1 million US stocks and to hedge the currency using a forward contract with a market value of $950,000, the hedge ratio is 95%. The hedge ratio changes because the values of the hedged assets and hedging instrument are not perfectly correlated. This is called basis risk.

²¹ The Organisation for Economic Co-operation and Development (OECD) and the International Monetary Fund (IMF) publish PPP statistics and implied exchange rates at www.oecd.org and www.imf.org.

²² The Economist invented the Big Mac Index in 1986. Check www.economist.com/content/big-mac-index for an interactive currency comparison tool.

²³ 1.66 = $4.79 ÷ £2.89.

²⁴ 1.554 = (1 + 0.50%) ÷ (1 + 0.25%) 1.55.

²⁵ The starting allocation is £50 equity and £50 bonds for every £100. After a year, the value of equities is £59 = £50 × (1 + 18%), of bonds is £48 = £50 × (1 − 4%) and that of each £100 is £107 = £59 + £48. New equity weight is 55.1% = £59 ÷ £107 and bond weight is 44.9% = £48 ÷ £107.