Risk Reward Measures

Question 1

Performance Measures

Answer 1

• Sharpe Ratio
• Information Ratio
• Sortino Ratio
• Maximum Drawdown
• Calmar Ratio

Question 2

Aspects of Performance Measures

Answer 2

In addition to profit/return a measure of risk is often incorporated e.g. the:
- standard deviation of returns (Sharpe)
- downside deviation (Sortino)
- maximum drawdown
You have in mind that low risk = consistent returns.

Question 3

Sharpe Ratio

Answer 3

A measure of risk-adjusted return widely used in finance.
Mean(returns - interest rates) / standard deviation(returns - interest rates)

A higher Sharpe Ratio indicates a better risk-adjusted performance. It suggests that the investment or portfolio generates more return per unit of risk.

Question 4

Information Ratio

Answer 4

Measurement of portfolio returns beyond the returns of a benchmark.

Mean(returns - benchmark returns) / standard deviation(returns - benchmarks returns)

Similar to Sharpe Ratio but allows benchmarks such as Treasury Bills or the S&P 500 index to compare to other opportunities.

A low tracking error means the portfolio is beating the index consistently over time.
A high tracking error means that the portfolio returns are more volatile over time and not as consistent in exceeding the benchmark.

Question 5

Sortino Ratio

Answer 5

Variation of a Sharpe Ratio that differentiates harmful volatility from total overall volatility.

Mean(returns - MAR) / downside deviation(returns, MAR)

Question 6

Downside Deviation

Answer 6

Root mean square of returns below the MAR.
Square returns, find mean, square root the result.

Question 7

Subsets of DD.

Answer 7

1. subset method: takes the root mean square only of those deviations where the return is below the MAR.
2. full method: it includes a 0 in the root mean square for every return above the MAR, and the deviation below the MAR for every other return.

Question 8

Maximum Drawdown

Answer 8

A measure of an asset’s largest price drop from a peak to a trough.

Question 9

Cumulative Return

Answer 9

Multiplication of returns +1, and subtract one at the end.

Question 10

Wealth Index

Answer 10

Same as cumulative return, except we do not subtract one.
max(cummax(wealthIndex)-wealthIndex)

Question 11

Calmar Ratio

Answer 11

FinalCumulativeReturn / MaximumDrawdown