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Risk and return

What are risk and return?

We like return and dislike risk, but risk is ever-present in all financial markets, and there is a positive relationship between risk and return. In other words risk and return are opposite sides of the same coin.

We know what return is: capital gains / losses + income (dividends or interest), and it is usually measured as holding period return42 (HPR):

where: P0 = buying price; P1 = selling price; I = income.

If annualized (AHPR):

where: n = years or fractions of a year.

But what is risk? It is the risk of the investment losing value (capital loss) or it not yielding an income or both. This possibility is encapsulated in a measurable concept:

The probability of the actual return (HPR) on an investment being different from the expected return (ER).

There are two broad sources of risk (that contribute to the probability of HPR being different from ER):

- Security-specific risk (aka unsystematic risk).

- Market risk (aka systematic risk).

Security-specific risk arises from the activities of the specific companies, and the industry of which they are a part, and may be seen as the major factors that affect the income flows of companies. Analysts generally categorize this risk-type into business risk (examples: prolonged labour strike, arrival of serious competition from offshore, harmful management decisions, changes in product / service quality); financial risk (when debt is utilized as a source of capital, and is used injudiciously by the company); and liquidity risk (the risk of the segment of the share market in which the relevant share is being illiquid so that fair market value cannot be obtained).

Market risk is made up of the risks that are inherent in the financial and/or economic system. This risk affects all markets and little can be done about it. Examples of this type of risk are: tax changes, upward changes in interest rates (interest rate risk), political instability (country risk), the declaration of a war (country risk), a major change in the exchange rate (exchange rate risk), a change in inflation (inflation risk).

Measuring risk and return

Measuring historical risk and return is straightforward, and it is best elucidated with an example using annual figures. Return over a year is HPR, and risk is the standard deviation of returns. This is a measure of the dispersion around the average return (= the arithmetic mean) in percentage terms. The formula is:

where

02 = variance of a set of values

X = each value in the set

M = mean (i.e. arithmetic average) of the set (mean return)

n = number in the set

0 = (o2)1/2 (i.e. square root of 02) = standard deviation.

Table 2 shows the hypothetical HPR returns on a share for the years 1 to 4, and the relevant calculations.

Calculation of historical standard deviation

Table 2: Calculation of historical standard deviation

This particular share has a mean return (M) of 8.75% and a standard deviation (0) of 13.77%. It will be obvious that the higher the standard deviation, the higher the percentage dispersion around the mean, and therefore the higher the riskiness of this share.

Relationship between risk and return

Figure 9 demonstrates the relationship between risk and return, and it is evident that the relationship is positive, i.e. the return required increases as risk increases. This is so because investors are risk averse. The relationship is represented by what is termed the capital market line (CML which is used extensively in portfolio literature). If investors were risk seeking (which would indicate a mental problem), the CML would be negatively sloped. The slope of the CML depicts the extent of additional return expected / required for additional each unit of risk assumed.

relationship between risk and return

Figure 9: relationship between risk and return

There is ample empirical evidence this relationship: money market at bottom left, bonds in the middle and shares top right. This is covered next.

Risk and return: the record

Fortunately, data is readily available on the risk and return relationship of the three main asset classes: shares, bonds and cash (i.e. money market).

Figure 10 shows the average annual returns and the standard deviations of the asset classes for a period of over 100 years for South Africa. The evidence is indisputable: higher returns are accompanied by higher risk (= dispersion around the mean return).

RSA: average annual returns & STD (108 years)

Figure 10: RSA: average annual returns & STD (108 years)

UK: average annual returns & STD (108 years)

Figure 11: UK: average annual returns & STD (108 years)

Similar numbers are recorded for the UK and the USA (Figure 11 and Figure 12).

It will be understood that when these average numbers are disaggregated into higher frequency numbers the variability of returns (risk) is revealed. Figure 13 shows the annual average returns for shares and Figure 14 shows the same for cash. Note that the scales are the same.

USA: average annual returns & STD (108 years)

Figure 12: USA: average annual returns & STD (108 years)

SA shares: annual returns (108 years)

Figure 13: SA shares: annual returns (108 years)

SA crash: annual returns (108 years)

Figure 14: SA crash: annual returns (108 years)

 
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