The Equivalence of Different Returns –The Sharpe Ratio

Question 1

The “Sharpe Ratio” is:

• A revenue metric divided by a risk metric
• A risk metric divided by a revenue metric
• A revenue metric
• A risk metric

Answer 1

revenue metric / risk metric

Question 2

In finance, it is useful to know both the return, and the volatility of return, of an investment, because:

• Returns can always be increased through leverage (borrowing money to make a portion of the investment) but this increases volatility, so returns cannot be evaluated in isolation, absent knowledge of their accompanying volatility.
• Higher volatility leads to higher returns.
• Volatility of returns is a measure of risk and avoiding risk is a fundamental aim of investing.
• Higher volatility leads to lower returns.

Answer 2

In finance, it is useful to know both the return, and the volatility of return, of an investment, because:

• Returns can always be increased through leverage (borrowing money to make a portion of the investment) but this increases volatility, so returns cannot be evaluated in isolation, absent knowledge of their accompanying volatility.

Question 3

In theory, an investor could generate any target return, simply by borrowing money to make a portion of the investment, and investing in an instrument that returns more than the risk-free rate. However, doing this would also:

• Require a more skilled manager
• Increase volatility of returns over the original instrument at the same rate that it increases excess returns.
• Inversely affect the discrete rate of return
• None of the above

Answer 3

Increase volatility of returns over the original instrument at the same rate that it increases excess returns.

Question 4

A money manager has $300 million to invest in stocks. They can expect a discrete return of 8%. The manager borrows an additional $100 million at 1% interest to invest in the same stock. Over a one-year period, by how many dollars did the manager increase the return by borrowing the $100 million?

• $7 million
• $6 million
• $8 million

Answer 4

$7 million

Question 5

annualized volatility of return

Answer 5

The standard deviation increases as the square root of time;

for example, if the standard deviation is 5.77% per month, than it can be estimated that it is 5.77Ò (12)% = 20% per year. If the the daily volatility is 1.26% per trading day, then we can estimate the 22 monthly volatility to be 1.26Ò (252)% = 20% per year.

Question 6

risk-free rate of return

Answer 6

• An investment return minus the return offered by stable governments for bonds in their own currency - this return is considered to have no default risk and so have zero volatility of return.

Question 7

manager skill

Answer 7

• Manager skill is usually defined as the ability to consistently generate an excess return over the manager’s benchmark, without excessive additional volatility - the risk-adjusted return should be better than the benchmark index.

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Question 8

sharpe ratio

Answer 8

• the ratio of a manager’s excess return over the risk-free rate (the manager return minus the risk-free return) divided by the volatility of the manager’s return.