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Investment- Risk-Adjusted Returns
Most investors aim to gain as much profit as possible for as little risk as feasible. Therefore, if two investments have a total return of 10% and the first investment has very little risk while the second one is quite dangerous, the first investment is better than the second one on a risk-adjusted basis.
Standard Deviation
Risk can take numerous forms. The risk we refer to throughout the rest of this module is investment risk. In Course 3, Investment Instruments, you learned that investment risk is commonly quantified based on the unpredictability of returns, and a common measure of variability is the standard deviation. The standard deviation of returns represents the variability of returns around the mean (or average) return — the larger the standard deviation of returns, the higher the variability of returns and the higher the risk.
There are at least two reasons why investors care about historical variability (the standard deviation of past returns). First, prior variability of returns might be indicative of how variable returns may be in the future. But it is vital to be aware that variability can alter over time and that there is no guarantee that future returns will behave like past returns.
Second, the variability of returns may impair the attainment of an investor’s objectives. Pension funds invest to create the returns necessary to pay their beneficiaries, insurance companies invest to generate returns to meet the claims on their policies, and people invest because they usually have a future spend in mind. Investing in a fund whose returns vary dramatically over time could possibly disturb investors’ plans. If returns are substantially negative one year, then the investors’ commitments, such as paying pensions, may be harder to meet.
Downside Deviation
Standard deviation is a measure of the variability of returns around the mean. Sometimes there is a positive deviation — that is, the return is more than the mean — and sometimes there is a negative deviation — that is, the return is less than the mean. Which of these two sorts of variation do you think investors would be more concerned about?
Well, psychologists and economists have discovered that investors loathe losses more than they prefer similar gains. So, investors can be moderately happy with earning an investment return of +10%, but quite upset about achieving a return of –10%. Because of this asymmetry in the way investors see the dispersion around the average, some investing professionals utilize a modified version of standard deviation known as downside deviation.
Downside deviation is computed in almost precisely the same way as standard deviation, except instead of utilizing all the deviations from the mean — positive and negative — downside deviation is calculated using only negative deviations. In other words, it is a measure of return variability that emphasizes primarily on outcomes that are less than the mean. Downside deviation may also be evaluated by focused on outcomes that are below a defined return target.
The following illustration demonstrates the standard and downside deviations of returns associated with investing in a diversified fund of global stocks and in a diversified fund of global bonds.
As we see, the downside deviations are lower than the standard deviations; this outcome is expected because downside deviations only consider the negative variances. Investors who are confined in their willingness or ability to endure losses will likely prefer the bond fund given its 3.8% downside deviation and reduced chance of losses against the equity fund with its 10.4% downside deviation and larger predicted losses.
Reward-to-Risk Ratios
Investors seek to earn a large return rather than a low return on their assets. That said, all things being equal, they also prefer lower risk (less variability of returns) over higher risk (more variability of returns).
In other words, investors are interested in optimizing the return on their investments while simultaneously striving to limit the dangers. That is, they choose investments that offer a high return per unit of risk — assets with a high reward-to-risk ratio. The measurement of a reward-to-risk ratio allows investors to compare the performance of one investment with another on a risk-adjusted basis.
A reward-to-risk ratio is a measure that takes the following basic form:
Most investors aim to gain as much profit as possible for as little risk as feasible. Therefore, if two investments have a total return of 10% and the first investment has very little risk while the second one is quite dangerous, the first investment is better than the second one on a risk-adjusted basis.
Standard Deviation
Risk can take numerous forms. The risk we refer to throughout the rest of this module is investment risk. In Course 3, Investment Instruments, you learned that investment risk is commonly quantified based on the unpredictability of returns, and a common measure of variability is the standard deviation. The standard deviation of returns represents the variability of returns around the mean (or average) return — the larger the standard deviation of returns, the higher the variability of returns and the higher the risk.
There are at least two reasons why investors care about historical variability (the standard deviation of past returns). First, prior variability of returns might be indicative of how variable returns may be in the future. But it is vital to be aware that variability can alter over time and that there is no guarantee that future returns will behave like past returns.
Second, the variability of returns may impair the attainment of an investor’s objectives. Pension funds invest to create the returns necessary to pay their beneficiaries, insurance companies invest to generate returns to meet the claims on their policies, and people invest because they usually have a future spend in mind. Investing in a fund whose returns vary dramatically over time could possibly disturb investors’ plans. If returns are substantially negative one year, then the investors’ commitments, such as paying pensions, may be harder to meet.
Downside Deviation
Standard deviation is a measure of the variability of returns around the mean. Sometimes there is a positive deviation — that is, the return is more than the mean — and sometimes there is a negative deviation — that is, the return is less than the mean. Which of these two sorts of variation do you think investors would be more concerned about?
Well, psychologists and economists have discovered that investors loathe losses more than they prefer similar gains. So, investors can be moderately happy with earning an investment return of +10%, but quite upset about achieving a return of –10%. Because of this asymmetry in the way investors see the dispersion around the average, some investing professionals utilize a modified version of standard deviation known as downside deviation.
Downside deviation is computed in almost precisely the same way as standard deviation, except instead of utilizing all the deviations from the mean — positive and negative — downside deviation is calculated using only negative deviations. In other words, it is a measure of return variability that emphasizes primarily on outcomes that are less than the mean. Downside deviation may also be evaluated by focused on outcomes that are below a defined return target.
The following illustration demonstrates the standard and downside deviations of returns associated with investing in a diversified fund of global stocks and in a diversified fund of global bonds.
As we see, the downside deviations are lower than the standard deviations; this outcome is expected because downside deviations only consider the negative variances. Investors who are confined in their willingness or ability to endure losses will likely prefer the bond fund given its 3.8% downside deviation and reduced chance of losses against the equity fund with its 10.4% downside deviation and larger predicted losses.
Reward-to-Risk Ratios
Investors seek to earn a large return rather than a low return on their assets. That said, all things being equal, they also prefer lower risk (less variability of returns) over higher risk (more variability of returns).
In other words, investors are interested in optimizing the return on their investments while simultaneously striving to limit the dangers. That is, they choose investments that offer a high return per unit of risk — assets with a high reward-to-risk ratio. The measurement of a reward-to-risk ratio allows investors to compare the performance of one investment with another on a risk-adjusted basis.
A reward-to-risk ratio is a measure that takes the following basic form:
The higher the value of the reward-to-risk ratio, the better the risk-adjusted return – that is, the higher the return per unit of risk.
A commonly used reward-to-risk ratio is the Sharpe ratio, so-called because it was initially suggested by Nobel Prize–winning economist William Sharpe.1 A fund’s reward is measured as the fund’s excess return, which is equal to the difference between the fund’s total return and the return on a ‘risk-free’ investment. The risk-free investment return is usually the return from investing in short-term government bonds because in most nations, government bonds are the assets that entail the lowest level of risk. The measure of fund risk is the standard deviation of the fund returns. The Sharpe ratio is determined as follows:
A commonly used reward-to-risk ratio is the Sharpe ratio, so-called because it was initially suggested by Nobel Prize–winning economist William Sharpe.1 A fund’s reward is measured as the fund’s excess return, which is equal to the difference between the fund’s total return and the return on a ‘risk-free’ investment. The risk-free investment return is usually the return from investing in short-term government bonds because in most nations, government bonds are the assets that entail the lowest level of risk. The measure of fund risk is the standard deviation of the fund returns. The Sharpe ratio is determined as follows:
Another often used reward-to-risk ratio is the Treynor ratio, introduced by Jack Treynor.2 The measure of fund reward is the same as that used in the Sharpe ratio, but the measure of fund risk is different. The measure of fund risk is the beta of the fund — beta being a measure of the fund’s systematic risk (also called market risk). Systematic risk was explored in the Investment Management module of this course. Thus, the Treynor ratio is a measure of the fund’s performance in relation to the degree of market risk assumed by the manager. The Treynor ratio is determined as follows:
Example: Calculation of Sharpe and Treynor Ratios
Suppose that over a year, the overall return of a fund was 10% and the return from investing in government bonds (‘risk-free’ assets) was 4%. Also assume that the standard deviation and beta of the fund’s returns over this period were 5% and 1.8, respectively.
The Sharpe ratio for this fund is
Suppose that over a year, the overall return of a fund was 10% and the return from investing in government bonds (‘risk-free’ assets) was 4%. Also assume that the standard deviation and beta of the fund’s returns over this period were 5% and 1.8, respectively.
The Sharpe ratio for this fund is
The Treynor ratio for this fund is
Each of these ratios can be compared with the same ratios for similar funds to evaluate the fund’s performance. As stated previously, the higher the value of the reward-to-risk ratio, the better the risk-adjusted return — that is, the higher the return per unit of risk.
The Sharpe ratio — along with other reward-to-risk ratios, such as the information ratio — is a key indicator for determining the quality of the returns provided by a fund. A fund with high returns but with significant risk might be said to have delivered worse-quality returns than a fund with similarly high returns but with substantially reduced risk. Reward-to-risk ratios, such as the Sharpe ratio, are one of the key quality control checks that investors can apply to their investment returns. Such ratios are also beneficial for comparing and analyzing investments.
The Sharpe ratio — along with other reward-to-risk ratios, such as the information ratio — is a key indicator for determining the quality of the returns provided by a fund. A fund with high returns but with significant risk might be said to have delivered worse-quality returns than a fund with similarly high returns but with substantially reduced risk. Reward-to-risk ratios, such as the Sharpe ratio, are one of the key quality control checks that investors can apply to their investment returns. Such ratios are also beneficial for comparing and analyzing investments.
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