Risk and Return from Investing - Investment Management by Charles P Jones

Chapter 6-Risk and Return from Investing

Q 6-1: Distinguish between historical returns and expected returns?

Historical returns are the returns that have realised in the past and expected returns are yet to materialise. Historical returns provide the investor with a trend upon which he builds up his future expectations.

Q 6-2: How long an asset must be held to calculate a TR?

TR implies total return. The two components of TR are periodic cash flows and capital gains. Period cash flow may be in the form of interest or dividends. Capital gain refers to the change—appreciation or depreciation—in price. While the capital gains can be earned in minutes, periodic cash flow income comes in intervals of no less than a quarter. Usually the interest payments are semi-annual, while the dividends may or may not be announced in a particular year. However, in certain conditions , an investor can earn a yield without keeping the security for too long. Such a phenomenon can take place, in case the investor buys the security of a company which is just about to announce dividends and sells immediately after receiving the dividend payment. No matter how the cash inflows are coming TR is usually calculated and expressed in annual terms.

Q 6-3: Define the components of total return. Can any of these components be negative?

Return on a typical investment consists of two components

1)      yield

2)      capital gain (loss)

Yield is the periodic cash flow (or return on investment in the form of interest or dividends). The issuer makes the payment in cash to the holder of the asset, but in some cases, this part of the return can also be in the form of additional securities, rather than cash. Capital gain (loss) is the appreciation (depreciation) in the price of the asset. It is also referred to as price change. It is the difference between the purchase price and the price at which the asset can be sold. For a short position, it is the difference between the sales price and the price at which the short position would be closed. In either case, a gain or loss would occur.

Total return can be obtained by adding up the two components of return. However an important thing to note is that yield can be either zero or greater than zero, but capital gain can be greater or equal to zero and can also be less than zero. If an investor purchases security at a higher price and sells it at a lower price, he would be having capital gains in negative which is a capital loss.

Q 6-4: Distinguish between total return and holding period return?

The total return refers to the sum of capital gains and periodic cash flows received during the holding period, whereas the holding period return refers only to the yield from holding the security and the gain or loss resulting from selling the security is not accounted for.

Q 6-5: When should the geometric mean returns be used to measure return? Why will it always be less than the arithmetic mean?

Geometric mean is used as a measure of central tendency when percentage changes in value overtime is involved. This measure is used to calculate the compound rate at which money actually grew overtime. Geometric mean would always be less than the arithmetic mean unless all the values are identical, having no deviation from the mean. Geometric mean takes into account the data dispersion, while the arithmetic mean only gives the central tendency. The relationship between the two means can be expressed as (1+GM)² = (1+AM)² –SD² , which also substantiates the fact that the two means cannot be equal unless the standard deviation equals zero.

Q 6-6: When should the arithmetic mean be used for measuring stock returns?

Arithmetic mean is the average return for a series and is used to measure the performance of a stock for a single period. Investors usually use arithmetic mean as a measure of central tendency when aggregating historical returns. For future returns geometric mean may be a batter measure.

Q 6-7: What is the mathematical linkage between the arithmetic mean and geometric mean for a set of security returns?

The mathematical relationship between the two means can be expressed as (1+GM)² = (1+AM)² –SD²

Q 6-8: What is the equity risk premium?

A risk premium is the additional return investors expect to receive or did receive by taking on additional amount of risk. Equity risk premium (ERP), in this context can be mathematically explained as the difference between the return on a stock and a risk free security. The level of equity risk premium increases as the share becomes more and more risky.

Q 6-9: If in a given period, the stocks provide more return than bonds, how can stocks be considered more risky?

The very fact that the stocks are providing more return gives evidence of their being more risky. A high return is a reward for taking a higher risk. Moreover, shareholders are the residual claimants in case of both profit distribution and liquidity of the firm, while the bondholders have a claim on assets prior to shareholders, hence the risk in shares is greater than in bonds.

Q 6-10: Distinguish between market risk and business risk? How is interest rate risk related to inflation risk?

The variability in the returns resulting from fluctuations in the overall market—that is the aggregate stock market—is referred to as market risk. Market risk includes a wide range of factors exogenous to securities, including recession, war, structural changes in economic and political conditions, law and order, as well as changes in the consumer preferences. On the other hand, the risk of doing business in a particular industry or environment is called business risk. For instances, chances that a particular industry is going to face stringent policies from the government can give rise to business risk.

Q 6-11: Classify the traditional sources of risk as to whether they are general or specific sources of risk.

Following traditional sources of risk fall in the category of general or systematic risk.

1. Interest rate risk: the variability of a security’s returns resulting  from changes in the market interest rates is referred to as interest rate risk. Other things being equal, the returns of the securities move inversely with the market interest rates. Interest rate risk affects bonds more directly than stocks and is considered as one of the major risks faced by bondholders.
2. Market risk: the variability in returns as a result of fluctuations in the overall market—that is the aggregate stock market—is referred to as market risk. Market risk includes a wide range of factors exogenous to securities, including recession, war structural changes in economy, political conditions, , law and order, and changes in the consumer preferences.
3. Inflation risk: A factor affecting all securities is the purchasing power risk—the chance that the purchasing power of invested dollars would decline. With uncertain inflation, the real return involves risk even if the nominal return is safe. This risk is also related to the interest rate risk, since he interest rate generally rises as the inflation increases, because lenders demand additional premium to compensate for the loss of purchasing power.
4. Exchange rate risk: Exchange rate risk is the variability in returns caused by currency fluctuations. Exchange rate risk is also known as currency risk.
5. Country risk: Country risk, also known as the political risk is important for investors. With more investors investing internationally, both directly and indirectly, the political and therefore economic stability and viability of a country’s economy need to be considered. United States, until the end of the last century was considered to have the lowest country risk, and Pakistan was quite risky. However, with the turn of the new century, the situation has immensely changed.

The following sources of risk fall in non-systematic category, also known as specific risk.

1. Business risk: The risk of doing business in a particular industry or environment is known as business risk.
2. Financial risk: Financial risk is associated with the use of debt financing by companies. The larger proportion of assets financed by debt, the larger the variability in returns, other things being equal.
3. Liquidity risk: Liquidity risk is the risk associated with the particular secondary market in which a security trades. The more uncertainty about the time element or concession to sell the security, the greater the liquidity risk.

Q 6-12: Explain what is meant by country risk?

Country risk, also known as political or sovereign risk, is significant to investors. With more investors investing internationally, both directly and indirectly, the political and economic viability of the country. United States is arguably considered to be the country with minimum political risk[1]. The political risk of Pakistan is assumed to be quite high due to intermittent shifts in power from democracy to dictatorship. When a country faces political turmoil, the government makes most of its policies on ad hoc basis and the investors cannot be certain about their returns from different sectors of economy, increasing the risk on their investments.

Q 6-13: Assume that you purchase a stock on Japanese market, denominated in yen. During the period you hold back the stock, the yen weakens relative to the dollar. Assume you sell on profit on the Japanese market. How will your return, when converted into dollars, be affected?

The return when adjusted to the currency change—a decline in this case—would result in a return less than what was calculated in yen denomination. If the change in the value of the currency is large, the profits may turn into losses when translated from yen to dollar denominations.

Q 6-14: Define risk. How does the use of standard deviation as a measure of risk relate to this definition of risk?

Risk may defined as the chance that the realised return would be different from the expected return. Usually, the investors build their expectations upon what they have experienced in the past. If they have secured a certain amount of return every year on a particular security, without any change for a considerable period of time, as in the case of treasury bills, there may not be any difference between the expected return and the realised return.

Standard deviation is a measure of data dispersion from the central tendency. If the values of a particular data were extremely high or low, such a data would have a higher standard deviation. As for the treasury bills, since the realised return has not been deviated from the expected return for a considerable period of time, the standard deviation of the returns would be zero, making the treasury bill a ‘risk-free security’.

Q 6-15: Explain verbally the relationship between the geometric mean and a cumulative index?

A cumulative index is a measure of increase in the level of wealth, whereas the geometric mean describes the average growth rate at which the wealth has increased.

Q 6-16: “If the geometric mean return for stocks over a long period has been around 11 percent and the returns on corporate bonds for some recent years have been averaged approximately at this rate. This leads some to recommend that investors avoid stock and purchase bonds because the returns are similar and risk is far less in bonds.” Critique this argument.

The statement acknowledges that the investors builds his hopes on his past experience, but ignores the fact that rational investors know that the stock market is about uncertainty and the historical cycle of returns may not repeat itself, even if the history does! They also know that a high return is the reward of assuming high risk. Even if the high risk securities like stock (in comparison to bonds) have not performed well in the past and the bonds did. It does not mean that the trend is going to continue forever. Moreover, it is quite likely that the bonds might be paying a high coupon rate because of high market interest rate prevailing at this time. The likelihood that the interest rates would remain where they are at the moment. If the interest rates fall in future, most of the bonds offering a high coupon rate, are likely to be called. If the bonds are called by the issuer, the bondholder is likely to get the call price, rather than the existing market price of the bond. This makes long term to exposure to bonds somewhat risky.

Q 6-17: Explain how the geometric mean and annual geometric mean inflation rate can be used to calculate inflation adjusted returns over the period 1920-2000?

If we divide the geometric mean rate of return for the period 1920-2000, by the geometric mean inflation rate during the same period, we would get the inflation-adjusted stock returns for the entire period.

Q 6-18: Explain the two components of the cumulative wealth index for common stocks. If we know one of these components on a cumulative wealth basis, how can the other be calculated?

The cumulative wealth index equals the per dollar cumulative total return and can be decomposed into two components, the yield component and the price change component. Since CWI is a multiplicative relationship, the total changes of the yield  and the price change can be multiplied to get the geometric mean of the total return.

G_TR = G_Y X G_PC

If we know the cumulative yield component and the cumulative wealth index, we can calculate the cumulative price change with the help of the following formula.

CPC = CWI/CYI, where CPC = cumulative price change, CYI = cumulative yield index, CWI = cumulative wealth index. Similarly, if the cumulative price change and cumulative wealth index are known, the cumulative yield index can be calculated by dividing the CWI by CPC.

Q 6-19: Common stocks have returned less than twice the compound annual rate of return for corporate bonds. Does this mean that the common stock are almost twice as risky as the corporate bonds?

Although risks and returns have a positive relationship, i.e., the returns increase as the risk increases, but that does not mean that that any change in risk would result in a proportional change in return. As we see in case of treasury bills, we can have a risk free return if we take no risk, however, when an investor takes some risk, he expects a premium as a compensation for taking risk. Doubling the risk would not double the return. Hence, risk of the securities need to be assessed considering a number of factors. One percent change in risk would not ensure that the change in return would also be one percent, it can be higher or lower depending upon numerous micro and macro environmental factors influencing the returns of a company.

Q 6-20: What does it mean if the cumulative wealth index for government bond over a long period is 0.85?

A value less than one for cumulative wealth index means that actual wealth of the investor has declined over the period from its initial level. Since the government bonds offer low returns, it is probable that if the CWI is adjusted against inflation, the level of wealth may decrease from its initial level.

Q 6-21: Fundamental to investing  is the control of the investment risk, while maximizing total investment return. Identify four primary sources of risk and explain the possible impact on investment returns?

The four primary sources of risk are

1)      Interest rate risk: The variability of a security’s returns resulting from the changes in the interest rates is referred to as interest rate risk. Other things being equal, returns move inversely with interest rates. Interest rate risk affects bonds more directly than common stocks and is a major risk faced by all bondholders.

2)      Inflation risk: a factor affecting all securities is the purchasing power risk. It is the chance that the purchasing power of the invested dollars would decline. With uncertain inflation the real return involves risk even if the nominal return is safe. This risk is related to the interest rate risk, since the interest rates generally rise as the inflation increases. It is because the investor demands additional premium to compensate for the loss of purchasing power.

3)      Financial risk: Financial risk is associated with debt financing by companies. The larger proportion of assets financed by debts, the larger the variability in return other things being equal.

4)      Liquidity risk: Liquidity risk is associated with particular secondary market in which the security trades. The more uncertainty about the time element and price concession, the greater the liquidity risk.

The first two sources of risk are classified as general risks. These risks affect the overall market and best of the investors with best of the portfolios might not be able to escape those risks. The last two sources of risks fall in the category of specific risks as they belong to the specific securities. Such risks are easier for investor to avoid.

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[1] The notion of United States being a politically risk-free country turned out to be a myth after September 11 incident. However some of the bitter critics had started questioning the US economic stability (which ensures the political stability) as the status of the country changed from being one the world’s largest lender to the world’s biggest debtor country in a span of few years.

e� ' i t �?� �� r offers to sell shares. The dealer profits from the spread between the two prices. The dealers also share profits with the brokerage firms for supplying the order. This is called payment of the order flow.

Q 5-23: Explain the difference between the initial margin requirement and the maintenance margin requirement?

The initial margin requirement implies the amount required to be invested to open a margin account and initiate a transaction. If the actual margin falls below the initial margin the account becomes restricted. However, the maintenance margin requirement implies that amount of equity which should be there at all times in order to keep the margin account functioning. If the actual margin falls below the margin account, the investor receives a margin call, which means that no transaction can take place without the investor’s placing more money in the account to replenish the account at least at the maintenance margin level.

Q 5-24: What is meant by having margin accounts “marked to market” daily?

By having margin accounts marked to market daily it means that actual margin of the investor’s account is calculated on a daily basis. This actual margin may be influenced by the changes in security prices in which the investor has invested using margin facility.

Q 5-25: Is there any link between margin account and short selling?

The link between margin account and short selling is such that without having a margin account an investor cannot short sell.

Q 5-26: Why do people say “The potential losses from short selling are unlimited”?

An investor sells short with the hope that the price of a stock will fall in future. If the price reaches minimum the investor will like to buy the share to close his short position. If the price of the stock increases instead, the investor can have losses. The minimum price that a stock can reach is zero, which means that there is a limit to which the profit off a short seller can increase. However, if the stock price starts increasing there is no limit to which the price may go and hence the potential losses for the short seller can be unlimited.

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[1] Unlike a limit order, where the broker tries to better the price, a stop order is used to hedge losses and therefore a price below the one mentioned in the order is acceptable to the investor. However, another kind of order is a stop-limit order, which combines the feature of a limit order and a stop-order, which is used to hedge losses in the same way as an ordinary stop order, however, the order is executed only if the investor’s mentioned price is met or bettered, otherwise no sale takes place, i.e., if the price has fallen below the limit the order would not be executed.