Chapter 4

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Investment Risk

The journey to your outcome

‘Risk means more things can happen than will happen.’

Elroy Dimson

Investing is risk. Risk is the flipside of return; there is no return without risk. The journey to your desired outcome is more likely to be bumpy than smooth.

In this chapter we will define what investment risk is, assess your appetite for risk, show how to measure risk and introduce a number of concepts that we will use throughout the book. Crucially, we will emphasise that to generate investment returns you must take investment risk.

Investment risk means you might not achieve your target outcome, even when making all the right decisions along the way with the available information at the time of making them. Investing evolves around forecasting the future. Do not believe ‘experts’ saying they can predict it – it is likely to be different from what they predicted. Since the future is uncertain, investing is risky.

When depositing money in a savings account in a big bank – a relatively safe investment, you will earn a rather low interest rate. It is likely to relate to the BOE’s base rate plus a spread. Say, for example, the base rate is 0.5% and the spread is 1.0%; the interest rate is 1.5%. Notwithstanding extreme circumstances, you will get the 1.5%.

BOE’s target inflation rate is 2.0%. Earning 1.5% on a deposit lags inflation. Whilst nominal return is 1.5%, real return is negative −0.5%. In real terms, you might lose money. You did not take a high risk so you do not deserve a high return – there is no free lunch.

A bank deposit or cash return is called risk-free. Well, it is not truly riskless. One risk is negative real return (inflation risk). Another risk is the bank going bust (counterparty risk), as Northern Rock or Lehman Brothers did in 2008. However, the British Government is unlikely to let any large, too-big-to-fail retail bank fail without protecting depositors.

Banks do not hold enough cash to repay all depositors in a bank run. The entire financial system can suffer a systemic shock due to loss of confidence when one large bank fails and all depositors want their money back. It can spread like waves after throwing a rock into a pond. To avoid this, the UK Government is likely to bail out any large financial institution on the brink of insolvency.¹

In 2008, the British Government announced a bank rescue package totalling about £500 billion. You, I and the rest of the British taxpayers became bank owners. And the banks survived, as well as the financial system.

The Financial Services Compensation Scheme (FSCS) protects deposits and other financial products held with firms authorised by the UK regulator, the Financial Conduct Authority (FCA). The FSCS protects deposits up to £75,000.²

To mitigate the risk of your bank going bust, divide deposits, including ISAs, across several large banks, putting up to £75,000 in each. Diversifying deposits across several financial institutions avoids putting all your eggs in one basket.

Remember these basket and eggs; we will come back to them later.

Earning a return above the risk-free rate requires taking an investment risk. One of investing’s fundamental principles is the higher the risk, the higher the expected return. The return is expected; not guaranteed. With higher risk come dangers, such as a chance of losing money. No pain, no gain; no guts, no glory.

What is investment risk?

The simplest definition of investment risk is the chance of not meeting your return objectives (shortfall risk).

For example, your target return is 5%. Alas, your portfolio returns 3%. It fell short of your objective. It does not matter that the return was positive; you did not lose money. What matters is the return was not what you targeted.

Frequently, people define risk as the chance of losing money. However, whilst this is clearly unpleasant and a true risk, a positive return can still miss your return objective. Also, what matters for long-term savers is average return over the entire time horizon. If you lose money in one year, but make it up later, then losing money is not detrimental.

Risk, like return, should be set against your individual financial goals and risk tolerance.

Risk tolerance

‘If you have trouble imagining a 20% loss in the stock market, you shouldn’t be in stocks.’

John Bogle

Risk tolerance is the risk level with which each person is comfortable. It consists of a subjective willingness to take risk and objective ability to take risk.

We are all different. Some people do not like taking risks. They work in a stable job, earning a stable salary. They enjoy relaxing holidays, nothing too extreme or challenging. And they like putting their money in a bank deposit without risking it. They are not willing to bear risk, they are risk averse.

For others, taking risks is normal, perhaps even exciting. They are entrepreneurs, running their own business. They enjoy the adrenaline rush of riding rollercoasters and extreme sports, such as parachuting out of aeroplanes and bungee jumping. They may enjoy gambling – try pulling them away from the roulette table in Las Vegas. And they are willing to bear risks when investing since they seek high returns.

Most people are somewhere in the middle of these two extremes. Rational investors are risk averse. Given two investments with the same expected return and different level of risks, rational investors will choose the less risky one. But we all have different degrees of risk aversion. Your personality and unique psyche determine your willingness to take risk. You should know your investor mentality and risk tolerance.

Questionnaires can help assessing your risk tolerance. One potential future development of asset management is robo-advisor – you will fill in an online risk questionnaire and a computer will automatically generate a portfolio matching your risk tolerance. However, before robo-advisors take over, whilst questionnaires can assist, they are generic. Think for yourself how you will feel when the stock market crashes or when the value of your portfolio fluctuates.

What are you going to do if the stock market falls by 20%? Does it make you anxious? Do you spend the night awake, thinking about how much money you lost today? Or do you keep calm and carry on?

You check your portfolio and it is down by 10% this month. How bad does it make you feel? Do you agonisingly regret investing in the stock market? What will you do?

The immediate instinct might be to sell all your stocks and rush to cash. But that could be a mistake. The stock market tends to rebound. By selling your stocks, you lose out when they fall and miss the rebound. Ouch and ouch.

The best way to know your investor-self is through first-hand experience. If you cannot stand the heat, get out of the kitchen. But first get into the kitchen to feel the heat.

A good rule of thumb is taking a risk level with which you can sleep well at night. You cannot live with worrying all day and all night about your portfolio. Saving for retirement is a multi-year project. Being concerned about your investments all the time is unhealthy. And you need health to accumulate wealth.

Whilst willingness to take risk is subjective, your ability to take risk is an objective measure of how much risk you can actually take.

For example, if you are 25 and you have just started working, you can take investment risk. A long investment horizon lies ahead, you cannot access your pension for a long time anyway and you probably earn a regular income. Even when losing, you have enough time to recoup losses. They are only paper losses until you realise them by selling.

However, this is not as straightforward as it seems. When you are young, you probably lack investing experience. Your total wealth is not much and losing on your portfolio hurts. So, your willingness to take risk may be low.

When you are 60, five years before retirement, your ability to take risk is low. If you make a big loss in your pension, time might be insufficient to earn it back. It might reduce your amount of money when retired, adversely impacting your standard of living.

Conversely, whilst your ability to take risk appears low, you may be a seasoned investor. Perhaps you own assets elsewhere to support you after retirement, such as properties to let. Maybe you have finished paying the mortgage on your home and your children do not need financial support. So, your willingness to take risk is high, as well as, perhaps, your ability.

The bottom line is that risk tolerance is individual and depends on your specific circumstances. Define what your risk appetite is, considering your willingness and ability to take risk. When assessing your risk tolerance, take a holistic view, considering all factors, such as time horizon, total wealth, likely reaction to market crashes and emotional state.

Risk measurement and management

Dealing with investment risk is done at three levels. The first level is to understand investment risks. Each type of investment comes with a number of different risks. You should qualitatively understand them. We discuss different risks throughout the book.

The second level is to measure risks. Risk measurement quantifies risks. We will review a number of risk measurements in this chapter.

The third level is to manage risks. Risk management is deciding which risks to take, which risks to mitigate and what actions to take to do so. We will cover risk management techniques in a dedicated chapter.

How to measure risk

The most common risk measure is volatility or standard deviation of returns.³ Standard deviation is a statistical measure of the dispersion of returns around the mean (average) return.

All you need to know about standard deviation is that when the return distribution is normal (symmetrical bell-shaped), two-thirds (68%) of returns fall within one standard deviation of the mean and 95% of returns fall within two standard deviations of the mean.⁴

For example, an investment’s average return is 8% with 15% standard deviation. Two-thirds of times, the range of returns is between −7% and 23% and in 95% of times the range is between −22% and 38%.^5,6 Figure 4.1 graphically illustrates it.

This investment’s returns are volatile. It can have very low (negative) and very high (positive) returns. You will be happy with the high returns, but can you tolerate the negative ones? Can you live with its downside risk?

If average return is what we would expect the investment to generate on average every year, we can transform standard deviation to downside risk.

When standard deviation is annualised (volatility per year) we can say that since 95% is 19 ÷ 20, in 19 in 20 years the return is likely to be above −22% (two standard deviations below the mean).⁷ But in 1 in 20 years the return is likely to be worse than −22%. Can you endure this? This is a way to assess risk tolerance.

These calculations assume a normal distribution. However, in real life, financial markets are not normally distributed. A 1-in-20 very negative return might occur more often than expected. Do not be surprised if this investment has a return worse than −22% every 5 or 10 years, more often than every 20 years. One shortcoming of standard deviation is that it assumes normal distribution.

Standard deviation does not say what the investment’s worst return might be. The investment in the example might generate a return of −30% or −50%. Extreme negative returns are called black swans or fat tails.⁸ These events do not occur often but when they do, it is painful.

Notably, standard deviation indicates the risk of missing your return objective. A wider spread of probable returns means the investment can deviate more from your expectations (target return) – its shortfall risk is higher.

Highly volatile investments can disappoint on the downside, as well as surprise on the upside with better returns than expected (upside risk). This is another shortcoming of standard deviation: it panelises investments symmetrically for both bad, negative returns and good, positive returns. You are concerned only about bad returns (downside risk).

Volatility is not a risk by itself. Do not confuse volatility with risk. According to finance theory, higher volatility should be compensated by higher expected returns.⁹ If you can sleep well at night with volatile investments, you may be rewarded with high returns over time. Volatility can be good.

For example, when investing in a volatile stock, it can generate high returns over time. The journey can be bouncy and stressful. But, even when down, the price can jump up. This is good volatility.

Bad risk that matters is permanent loss. That is the downside risk you cannot or do not have time to recoup.

For example, when investing in a stock or bond of a company with a volatile business and the company goes bust, your stock or bond can become worthless. Your investment is permanently impaired. This is bad volatility.

Bad volatility might also cause you to make bad investment decisions. When volatile markets fall, you might sell near the bottom because you do not know how further down they might drop. The volatility is not bad per se, but it results in bad investor behaviour.

In this sense, the timing of volatility is critical. Volatility could be fine if you have time. But if you are just approaching retirement, for example, you cannot afford a big loss since time is running out. You may need to cash in on the investment soon – this makes you a forced seller.

Risk tolerance and time horizon are strongly linked. Volatility can be good when time horizon is long, but bad when time horizon is short. Timing is everything.

The timing of returns also matters. Large negative returns have bigger impact closer to retirement, when the amount of savings is relatively large, than many years before retirement, when the amount of savings is relatively small. The timing of returns is called sequential risk. The final wealth outcome is a function of sequential risk and investment risk.

Different asset classes have different volatility levels. Equities are volatile. Their volatility is around 15% for developed market equity (such as UK stocks) and over 20% for emerging market equity (such as stocks in Brazil, Russia, India and China). Government bonds (such as UK gilts) have a volatility of about 5%. Cash has volatility below 1%.

Because equities are riskier than bonds and cash they offer higher expected returns. Why would any rational investor invest in a risky asset unless it offers higher potential returns? The higher returns are ‘expected’ and ‘potential’ since they are not certain. This higher equity return is called equity risk premium.

By blending different assets in different proportions you can tune your portfolio’s volatility to match your risk tolerance. More stocks means higher volatility. Fewer stocks and more bonds and cash mean lower volatility. You can readily quantify your portfolio’s risk level using volatility as a single metric.

It is not perfect. Volatilities change – they tend to spike up when markets are in stress and come down when markets are calm. And volatility has the shortcomings we mentioned (assuming normal distribution, undiscriminating between upside and downside). However, using volatility is a simple, pragmatic solution to measure risk and align your portfolio’s risk with your risk tolerance.

Another reason to blend different imperfectly correlated investments, or investments that behave differently, is diversification. Through diversification volatility is reduced. Diversification is a proven way to mitigate risk.

Surely, you remember the basket and eggs. It is so important that, later, we dedicate a whole chapter to diversification.

Beta

Beta (Greek β) is another popular risk metric.¹⁰ It measures volatility with respect of an index, reflecting an investment’s tendency to respond to index movements.¹¹ Put differently, beta is the correlation between the investment and index times the ratio between the investment’s volatility and the index’s volatility.

A beta of 1 indicates the investment’s price tends to move in the same direction and magnitude as the index. A beta below 1 indicates the investment tends to be less volatile than the index. A beta above 1 indicates the investment tends to be more volatile than the index.

A negative beta indicates the investment tends to move in the opposite direction of the index. A beta of zero indicates the investment is market-neutral – its returns tend to be independent of those of the index. A high positive beta (above 0.70) indicates the investment is directional – it tends to move in the index’s direction and magnitude.

For example, investment A has a beta of 1.2. This directional investment tends to be 20% more volatile than the index. When the index moves up 10% or down 10%, investment A tends to move 12% or −12%, respectively.

Investment B has a beta of 0.2. When the index moves up 10% or down 10%, it tends to move only 2% or −2%, respectively. This is a non-directional investment. It is not completely market-neutral, but certainly not directional.

Since our focus is not on risk relative to a market or an index, we are not going to use beta as a risk measure. However, it is important to understand the concept of beta as a source of risk, and therefore return, due to exposure to the market.

A directional investment has beta exposure. Some of its risk and return come from market movements. A market-neutral investment has no beta exposure. Its risks and return come from other sources, rather than market movements.

Fixed income risks

Whilst for investments such as equities volatility is the common risk gauge, fixed income investments (bonds) have other risk measures, in addition to volatility.

Bonds pay investors a series of cash flows in the form of coupons (interest), typically twice a year, and then repay the loan’s principal at maturity.

For example, you buy a 10-year gilt (UK Government bond) with a nominal face value (principal) of £1,000 and a 5% coupon. On 7 March you receive £25 (half of the annual 5% coupon). On 7 September you receive another £25. You keep receiving such coupons every six months until, upon the gilt’s maturity date, you receive £1,025, which is capital repayment and final coupon.¹²

Fixed income investments are sensitive to three main types of risks:

1. Interest rate risk.
2. Inflation risk.
3. Credit risk.

Interest rate risk

The price of a bond, and that of most investments, reflects the present value of its future cash flows. Money today is worth more than money tomorrow. You have an opportunity to deposit it at a bank or invest it to enjoy a return – this is time value of money. By not having it today you incur an opportunity cost.

Calculating the present value of future cash flows requires discounting them to today’s value by applying the expected rate of return you could have earned – the discount rate.

For example, you anticipate receiving £1,000 in five years. If you had the money today you could have invested it, expecting to earn 5% per year – this is the discount rate, which is the compound annual growth rate. In five years’ time, your £1,000 would have reached an expected future value of £1,000 × (1 + 5%)⁵ = £276.3.

Using the same calculations, but in reverse, if the future value in five years is £1,000, the present value is £1,000 ÷ (1 + 5%)⁵ = £783.5. The future value of £783.5 in five years is £1,000.¹³

One challenge with present value calculations is that the amounts and timing of cash flows are not always known in advance. Another challenge is that the appropriate discount rate typically is not certain. It should reflect the investment’s risk level – the uncertainty of cash flows, or the required rate of return (RRR) that investors demand as compensation for holding the investment.

For example, for a low-risk bank deposit, RRR could be 2% – you know this is the return you will earn. But for a volatile stock the RRR could be 8% – you do not know the return you will realise. You should require a higher return or a risk premium for a riskier investment. Otherwise, why should anyone rational accept its risk?

Present value calculations demonstrate another important principle of investing: high price today means lower RRR, whilst low price today means higher RRR.

For example, two identical investments pay a single £100 cash flow in 12 months. The price of investment A is £95 whilst the price of investment B is £90. The RRR of expensive A is 5% and that of inexpensive B is 10%.¹⁴

When an asset’s price is rich, expect lower future returns. When an asset’s price is cheap, expect higher future returns, all else being equal. Pay careful attention to price when buying investments. High price means borrowing returns from the future.

Discount rate is made of the market’s prevailing interest rate plus a spread, reflecting each particular investment’s risk. In other words, it includes the risk-free rate of return for the appropriate horizon (such as BOE’s base rate or 10-year gilt yield) plus a risk premium to compensate investors for risk.

As bonds produce a relatively foreseen stream of future cash flows, bond price closely reflects these cash flows’ present value. Rising interest rates mean an increasing discount rate and decreasing bond price. Falling interest rates mean a decreasing discount rate and increasing bond price – an inverse relationship between interest rates and bond price.

Interest rate risk, therefore, is a potential fall in bond price, due to rising interest rates. For example, if the base rate is 0.5% and the BOE hikes it to 1%, bond prices may fall.

Interest rate risk is relevant to most assets that produce future cash flows, not only to bonds.¹⁵ If the current price of an asset is the present value of its future cash flows, rising interest rates mean higher discount rate and potentially lower price.

Central banks, such as the BOE in the UK, set short-term rates. However, market forces of supply and demand set long-term rates. When more buyers than sellers buy government bonds with a maturity of 10 years, for instance, they push their price up. When price goes up, bonds’ interest rate (yield) goes down. When more sellers than buyers sell 10-year bonds, they push their price down and yield up.

Another way to look at it is that when a bond is first issued, it offers a certain coupon rate. Demand sets its price and yield. This yield is appropriate for current market conditions. Say market rates rise. The bond is not attractive any more because its yield is not competitive now that rates elsewhere are higher. Supply surpasses demand until the price of the bond adjusts downward, increasing its yield so it is competitive again. This is interest rate risk.

Duration is a common interest rate risk measure. Modified duration measures the sensitivity of bond price to changes in interest rates.¹⁶ Measured in years, duration reflects the weighted average maturity of cash flows.¹⁷

The longer the maturity, the longer is the duration. The smaller the coupons, the longer the duration, since the weight of capital repayment at maturity is larger. A longer duration means the bond price is more sensitive to changes in interest rates.

For example, a 10-year bond with a 5% coupon has a duration of 7.8 years. A similar bond with a 7% coupon has a duration of 7.4 years. Duration is shorter than maturity, unless it is a zero-coupon bond, which pays no coupons, so its duration equals its maturity.

Under certain assumptions (small, parallel shift of all interest rates across different maturities) change in bond price equals minus the change in interest rates times the bond’s duration.¹⁸

For example, the duration of a 10-year gilt is 8 years. A 0.50% or 50 basis points (per cent of a per cent or 1 , 10,000) increase in interest rates means the bond price falls by about 4%.¹⁹

Because long-duration bonds are riskier than short-duration ones, long-maturity bonds must offer higher yields to compensate investors for risk. Otherwise, why would investors take the risk? This principle repeatedly pops up – higher risk requires higher return.

This is a similar logic to time deposits at banks and fixed rate cash ISAs. Banks pay a higher interest rate compared with regular deposits as you commit your money for a longer time. You are compensated for giving up some flexibility.

This is another principle: flexibility and optionality are valuable. Usually, you pay for flexibility and you can get paid for giving up flexibility. Here, you ‘sell’ the flexibility of your money to the bank. You give up the option of taking it whenever you want.

The compensation for long duration is called term premium. You should earn a higher return for investing for a longer term. Term premium reflects the higher uncertainty of future cash flows and the price of longer duration bonds (compensation for the risk of unexpected spike in rates).

Inflation risk

Inflation erodes the purchasing power of bonds’ cash flows. Bond price incorporates expected inflation. Bonds’ future cash flows are nominal, so expected inflation is part of the nominal discount rate when calculating their present value.²⁰ However, realised inflation might deviate from expected inflation. Therefore, bond yield and price are sensitive to inflation risk.

For example, to calculate the present value of a 10-year gilt paying a 5% semi-annual coupon with a £1,000 face value, you apply a 2% discount rate, reflecting expected future short-term rates of 1% and 1% inflation. The bond price is £1,272.

Due to an unexpected jump in oil price, inflation is now expected to rise to 3%. The new discount rate is 4%. The bond price drops to £1,085. You also expect interest rates to increase due to higher inflation, further increasing the discount rate and decreasing the bond price.

The longer the maturity, the higher is the risk of inflation deviating from expectations. Also, inflation’s potential impact on cash flows is larger. Long-term bond rates reflect, among others, the market expectations of future short-term interest rates and inflation.²¹

When the economy is growing, inflation is expected to rise due to increased aggregate demand for goods and services. Central banks are likely to raise short-term rates to control inflation. So bond price should suffer when the economy grows due to both interest rate risk and inflation risk. The opposite should occur when the economy slows down.

Inflation risk is not exclusively relevant to bonds. It is a risk of most investments. However, the prices of some investments, such as inflation-linked bonds and property, are linked to changes in inflation. Such investments mitigate inflation risk.

Credit risk

Credit risk is the chance the bond’s issuer will default on its obligations in accordance with agreed terms. A default includes not paying all payments – nothing at all or smaller amounts following a debt restructuring (haircut), or delaying the timing of payments.

When buying a bond you are the lender (creditor). You assume credit risk that you will not get fully paid or paid on time as you were promised.

Gilts issued by the British Government have negligible credit risk. The British Government will not default, or at least it is extremely improbable. It has a reputation to maintain. Otherwise, it will not be able to borrow at low interest rates. Its creditors will demand higher rates as compensation for higher risk. It can always increase taxes, borrow more or print money to pay off its debt.

Bonds issued by a corporation or a government of a country that runs into financial difficulties might default. A corporation can go bust and a country can run out of money. Argentina, Greece and Russia are examples of countries notoriously defaulting on their sovereign debt.

For assuming default risk you are compensated with a higher interest rate compared with gilts. This higher rate is credit risk premium.

Credit risk is pertinent not only to bonds, but also to other investments. When letting a flat, for example, your tenant can default on rent.²² This is credit risk.

When taking out a mortgage to buy a house, the lending bank is your creditor. It undertakes a credit risk with respect of you. However, it minimises its risk since your house is the collateral for the loan. Because property is a full collateral for the entire loan, it is secured and mortgage rates are lower than other, more speculative loans. Mortgage rates reflect the price of risk.

One of the reasons for the 2008 credit crunch was sub-prime lending. Banks irresponsibly handed out mortgages to borrowers with a questionable ability to pay off their loans, without adequate collateral. They mispriced risk by not demanding appropriately high mortgage rates.

Liquidity risk

One of the riskiest, but often-ignored, investment risks is liquidity risk. It is the ability or inability to sell investments when you want at a reasonable price. It captures the time and costs associated with liquidating investments into cash.

Cash is the most liquid medium of exchange and store of value. You cannot go to the supermarket with stocks and bonds – you need cash. Therefore, it is important to be able to turn investments into cash.

Different types of investments generally have different degrees of liquidity. Cash, gilts and government bonds of countries such as the USA and Germany are the most liquid. Stocks of large companies traded in developed markets and highly rated corporate bonds are liquid. Stocks of small companies, stocks traded in emerging markets and lowly rated corporate bonds are less liquid. Property and ownership rights in private businesses (private equity) are illiquid.

Similar to other investment risks, the market must attract investors to accept risks by offering returns. The reward for liquidity risk is liquidity premium.

Investors with a truly long investment horizon, such as savers for retirement, can shoulder liquidity risk since they do not need cash quickly. This allows them to harvest the liquidity premium. For example, part of the return of property should reflect its illiquid nature.

Illiquidity means inflexibility. When buying an annuity, for example, you receive a guaranteed stream of income that can satisfy part of your financial needs. However, an annuity is illiquid – it is inflexible, you cannot sell it (although this may change when an annuity secondary market is introduced). This is its main trade-off.

Linking risk and return

As you can see, one of the basic philosophies of investing is that risks should be compensated by returns.

For example, investment A’s expected return is 5% with 10% volatility. Investment B’s expected return is also 5%, but with 15% volatility. Nobody will buy investment B since it has the same expected return as that of investment A, but with a higher risk.

Lack of demand for investment B pushes its price down, until its expected return increases to 7%. Now, investment B is interesting for investors seeking higher returns than that of investment A and willing to accept its higher risk.

Investing is all about taking risks. Risk is not necessarily a bad thing. Without risk you could not earn above risk-free returns. Risk is a scarce resource you should embrace as it generates returns.

For example, saving for retirement, you aim for a £550,000 target portfolio size. Given your income, contributions and time horizon, your portfolio needs to return 5% per year to reach your goal. The interest rate on cash deposits is 2%. The only way for your portfolio to generate a return above 2% is by taking investment risk. Without risk you could not reach your target.

By blending different risk factors you can benefit from different risk premiums. If one does not deliver – nothing is certain, it is a risk – others may do so. Once again, do not put all your eggs with a single risk.

Investing needs courage. However, it also needs patience. When taking risk you can go through rough times, seeing your risky investments disappointingly losing. Not everyone can easily undergo such bad patches. It depends on your risk tolerance.

The principle of high risk/high return works in practice. Empirically, riskier investments have generally generated higher returns than safer ones. However, it heavily depends on the specific time period. There are times when riskier investments do much poorer than safer ones. This is the reason it is called risk.

This all means you should take controlled risks in your portfolio. It is the only way to generate returns in excess of the risk-free rate. Harvest the equity, term, credit and liquidity risk premiums to benefit from different sources of returns.

Risk-adjusted performance

Since return and risk are linked, it is helpful to combine them into one ratio. Sharpe ratio, called after its developer Nobel laureate William Sharpe, is a common risk-adjusted return measure.

Sharpe ratio is the average return earned in excess of the risk-free rate per unit of volatility (absolute risk).²³ Higher Sharpe ratio means the investment generated higher reward per unit of risk.

For example, an investment generated a 10% return, the risk-free rate is 2% and the investment’s volatility is 16%. The Sharpe ratio is 0.50.²⁴

Sharpe ratio can vary substantially across different investments and times. However, a general rule of thumb for a diversified portfolio is assuming a Sharpe ratio of 0.50. This is useful to link the return objective to the risk objective.

For example, your return objective is 5% per year, and the risk-free rate is 1%. Assuming a Sharpe ratio of 0.50, you will need to tolerate a volatility level of 8%.²⁵

Absolute versus relative risk

Absolute risk focuses on how much you might lose independent of any benchmark or reference. For instance, volatility and duration are absolute risk measures. When buying a stock or an equity fund, one concern is that it can lose money. When buying a bond, interest rates might shoot up and your bond price might drop. This is absolute risk.

Relative risk focuses on potential losses compared to a benchmark or your investment objectives. For example, when investing in an actively managed equity fund, its fund manager aims to outperform a benchmark. The manager’s job is justifying the fee paid for the potential return in excess of the benchmark.

To outperform the benchmark, the manager needs to perform differently from it. To do so, the fund must hold different securities or in different weights from those in the benchmark; otherwise, the fund and benchmark’s performance will be identical. The manager must take a tracking risk with respect of the benchmark. This relative risk is often measured as tracking error.

Tracking error is relative standard deviation. The difference between them is that standard deviation uses absolute returns whilst tracking error uses relative returns (the difference between the returns of the fund and benchmark).²⁶

Tracking error is a function of the correlation between the fund and the index, as well as their volatilities.²⁷ Higher volatilities and lower correlation lead to higher tracking error. It is more difficult to perform in line with a volatile asset – it is like hitting shooting ducks in a funfair; a static bullseye is easier to hit.

Tracking error and standard deviation have the same statistical properties. For example, when tracking error is 2%, assuming a normal distribution of relative returns, in two-thirds (68%) of times relative return is between −2% and +2% (one tracking error) and in 95% of times relative return is between −4% and 4% (two tracking errors).

Passive index trackers aim to minimise tracking error relative to their benchmark. Do not expect passive trackers to underperform or outperform the index. They should track it!

For example, a FTSE 100 Index tracker should fall by about 10% when the index falls 10%. If the tracker falls by only 5% then it is good, since it outperformed, but really it is bad, since it does not do what it says on the tin. Good returns are not always good. Investments should do what they are supposed to do, not to surprise you.

Information ratio

Similar to Sharpe ratio in absolute return/risk space, in relative space a popular risk-adjusted return measure is information ratio. It is calculated by dividing relative return (fund’s return minus benchmark’s return) by tracking error.²⁸ Information ratio measures the value added by active management considering risk.

For example, a fund returned 10% whilst its benchmark returned 8%. If the tracking error was 2%, then the information ratio is 1.0.²⁹ An information ratio above 0.50 is considered good.

The need to take risk

When saving for retirement the risk level to bear is not only about your risk tolerance, but also about your need to take risk. Your goal is saving an amount of money by your retirement. This amount needs to support you financially for the rest of your life.

The amount is a function of three variables:

1. Time.
2. Contributions.
3. Net return.

Given time and contributions, you need a certain target net return. To achieve this return, you need to accept a certain risk level.

Whether you are happy with this risk or not, it is needed. The only other ways to achieve the target amount without taking investment risk are:

1. Save over a longer time period by either starting earlier (which is impossible from where you are now) or deferring retirement.
2. Increase contributions.
3. Settle for a lower standard of living post retirement by reducing the target saving amount.
4. Minimise costs and taxes (increase efficiency to reduce bleeding of money in pension).

For example, you are 40 and want to retire at 55 (time is 15 years). You and your employer contribute £40,000 per year (the annual allowance benefiting from a tax relief). You aim for £1 million when retiring. To reach your target, you need an annual average return of 6.4%.³⁰ Assuming a 0.50 Sharpe ratio and a 1% risk-free rate, you need to accept volatility of 10.8%.³¹

Your circumstances and objectives dictate the risk level you must tolerate. If risk is too high, you can postpone retirement to 65, for example. By extending time by 10 years, keeping contributions constant, you actually need nil return and nil investment risk (ignoring inflation risk). However, postponing retirement by 10 years is not a privilege or a desire of everyone.

Not taking sufficient risk is a risk.

Longevity risk

The average life expectancy continues to increase due to ongoing medical advancements, better healthcare and lifestyle education. Your life expectancy depends on your current health and heredity, among other factors (such as luck).

A man reaching age 65 in 2015 can expect to live, on average, for another 18 years, according to the Office for National Statistics (ONS). This is compared to six years for men reaching 65 in 1980. Women at 65 today can expect to live another 21 years, compared to 12 years in 1980.

Longevity risk means you might outlive your assets, as your time horizon may be longer than you realise. Be prepared to live a long time, ensuring you have enough money to maintain your lifestyle.

This is one of the most important risks when planning for retirement. Running out of money (financial ruin) could be dreadful.

Risk is a multi-faceted, multi-dimensional concept. When thinking about it, consider the range of potential results, how much you might lose, and the chance of a permanent loss. Reflect whether you can sell investments, if you want to do so. Contemplate whether the amount you have accumulated is sufficient, even if you live longer than expected. And ensure risk is in line with your risk tolerance and the returns you require to achieve your financial goals.

It is always more pleasant focusing on returns and the upside. However, focusing on the potential loss if things do not turn out as hoped for is more valuable.

Summary

• Earning a return above the risk-free rate needs taking investment risk, which is the chance of missing your return objective.
• The most important risk is shortfall risk – the chance of realised return falling short of your target return.
• Risk tolerance is your willingness and ability to take risk.
• Investing’s true risk is permanent loss. Volatility is not bad, as long as your time horizon allows recouping losses. When time horizon is short, appetite for volatility should wane. Timing is everything – you cannot afford to lose a lot just before needing the money.
• Different assets have different volatilities. By blending them in different proportions construct a portfolio with a risk level matching your risk tolerance.
• Three main risks in fixed income are interest rate, inflation and credit risk. Liquidity risk is relevant to any illiquid asset.
• Higher risks should come with higher returns, but not always.
• You need to take risk. Calculate your target savings amount at retirement. Achieving this amount is a function of time, contributions and net return. Given time and contributions, target return dictates a certain risk level.
• Consider longevity risk when saving and investing for retirement. Avoid running out of money after retirement.

Notes

¹ This can cause a moral hazard. Bankers can take excessive risks since they know that the government and the public bear the burden of these risks.

² For compensation limits and other information on FSCS visit www.fscs.org.uk.

³ Standard deviation (σ, sigma) is the square root (✓) of the sum (Σ) of the squared distances of each return i (r_i) from the mean return (μ mu), divided by the number of returns (N). σ = ✓Σ[(r_i − μ)² ÷ N].

⁴ 99.7% of returns fall within three standard deviations of the mean. Two-standard-deviation (2-sigma) event has a probability of 2.275% to occur or every 44 days. Three-sigma event is expected to occur once every 741 days, 4-sigma event every 31,560 days (126 years) and 5-sigma event every 13,932 years.

⁵ −7% = 8% −15%; 23% = 8% + 15%.

⁶ −22% = 8% −2 × 15%; 38% = 8% + 2 × 15%.

⁷ To annualise standard deviation based on daily returns, multiply it by the square root of 252 (number of business days in a year). If it is based on monthly returns, multiply it by the square root of 12 (number of months in a year).

⁸ They are called fat tail since there are more returns in the tails of the distribution than predicted by a normal distribution; the tails of the distribution are fatter than normal.

⁹ To be precise, according to the Capital Asset Pricing Model (CAPM) undiversifiable volatility, or market risk as measured by beta, should be compensated by higher returns.

¹⁰ β = Cov(r_i, r_m ÷ Var (r_m) where r_i is the returns of investment i, r_m is the returns of the market, Cov is covariance and Var is variance. Another way to define beta is β = ρ_{i, m}(σ_i ÷ σ_m). Beta is the slope of a linear regression line when regressing investment’s returns on index’s returns.

¹¹ The index could be an index representing an equity market, such as FTSE 100 Index, a bond market, other asset classes or a blend of asset classes.

¹² The London Stock Exchange publishes on its website at www.londonstockexchange.com ‘A Private Investor’s Guide to Gilts’, which includes detailed explanations on gilts.

¹³ £1,000 = £783.5 (1 + 5%)⁵. PV = Σ[CF_t ÷ (1 + r)^t]; where PV is present value, CF_t is cash flow at time t and r is the rate of return.

¹⁴ £95 = £100 ÷(1 + 5%); £90 = £100÷(1 + 10%).

¹⁵ Unless their cash flows change with interest rates, such as those of Floating Rate Notes (FRNs).

¹⁶ Duration measures how much time it will take the bond’s cash flows to repay the bond’s price to investors. Modified duration measures the sensitivity of bond price to changes in interest rates. ΔP = −DΔy where ΔP is change in price, D is modified duration and Δy is change in yield.

¹⁷ Check Investopedia at www.investopedia.com for a free duration calculator. One of the inputs of the calculator is yield (yield to maturity), which will be explained in Chapter 9 in the section ‘Fixed income’.

¹⁸ Bond’s duration changes when interest rates change. Convexity measures the sensitivity of duration to changes in rates. Using duration and convexity can improve estimating bond price sensitivity to changes in rates compared to using only duration. ΔP = −DΔy + 0.5CΔy² where C is convexity.

¹⁹ −4% = −0.5% × 8.

²⁰ When cash flows are real the discount rate should be real and when cash flows are nominal the discount rate should be nominal.

²¹ The shape of the term structure of interest rates is explained by three theories. Long-term rates reflect expected future short-term rates (pure expectations hypothesis), liquidity premium (liquidity preference hypothesis) and supply and demand of different bond maturities (segmentation hypothesis).

²² Some ways landlords can protect rental stream include due diligence on tenants (credit checks and referencing), rent deposit, post-dated cheques, guarantees, guarantors and interest on late payments.

²³ SR = (r −r_f) ÷ σ where SR is Sharpe ratio, r is the asset’s return, r_f is the risk-free rate and σ is the asset’s volatility. SR can be based either on expected, future, ex ante return and risk or realised, historic, ex post return and risk.

²⁴ 0.50 = (10% − 2%) ÷16%.

²⁵ 8% = (5% − 1%) ÷ 0.50.

²⁶ Tracking error = standard deviation (r_i − r_b where r_i is the series of investment returns and r_b is the series of benchmark returns. TE = ✓(σ²_p + σ²_b −2ρ_{p, b}σ_pσ_b) where σ_p and σ_b are the volatilities of the portfolio and benchmark and ρ_{p, b} is the correlation between them.

²⁷ Determinants of tracking error are number of securities in the portfolio (those in the benchmark and those not in the benchmark); size, style and sector deviations from those of the benchmark; beta and benchmark volatility.

²⁸ IR = (r_i −r_b) ÷ TE_{i, b} where IR is information ratio, r_i is investment’s return, r_b is benchmark’s return and TE_{i, b} is tracking error of the investment with its benchmark.

²⁹ 1.0 = (10% −8%) ÷ 2%.

³⁰ Using the savings calculator of the Citizens Advice at www.citizensadvice.org.uk, to reach £1 million in 15 years the monthly contributions are £3,333, which is £40,000 per year.

³¹ 10.8% = (6.4% −1%) ÷ 0.50.