Risk-Adjusted

Lesson

Risk-adjusted returns are used to evaluate an investment portfolio's performance by considering the level of risk involved. This allows investors to compare the performance of different investments.

Practice Question #1

Which of the following measures of risk-adjusted return considers an investment's sensitivity to market movements?

Terms

Risk-adjusted return:

A measure of an investment's return relative to its risk.

Sharpe ratio:

A measure of risk-adjusted return that divides the excess return of an investment by its standard deviation.

Sortino ratio:

A measure of risk-adjusted return that divides the excess return of an investment by its downside deviation.

Treynor ratio:

A measure of risk-adjusted return that divides the excess return of an investment by its beta.

Jensen's alpha:

A measure of an investment's risk-adjusted return that compares its actual return to its expected return based on its beta and the market return.

Information ratio:

A measure of risk-adjusted return that compares the excess return of an investment to its tracking error.

Standard deviation:

A measure of the volatility of an investment's returns.

Beta:

A measure of an investment's sensitivity to market movements.

Downside deviation:

A measure of the downside risk of an investment's returns.

Tracking error:

The difference between an investment's return and the return of a benchmark index.

Practice Question #2

What is the primary difference between the Sharpe ratio and the Sortino ratio?

Historical Example

In the late 1990s, many investors were attracted to technology stocks due to their high returns. However, these stocks also had high levels of risk, which became apparent during the dot-com crash in 2000. Investors considering risk-adjusted returns would have been better prepared for this downturn.

Practice Question #3

Which of the following measures of risk-adjusted return compares an investment's actual return to its expected return based on its beta and the market return?

Real-World Example

An investor is comparing two mutual funds. Fund A has an average annual return of 10% and a standard deviation of 15%, while Fund B has an average annual return of 8% and a standard deviation of 10%. By calculating the Sharpe ratios for both funds, the investor can determine that Fund B has a higher risk-adjusted return and may be a better investment choice.

Rhyme

"For excess return atop risk-free rate, Sharpe ratio's the measure, isn't it great? Sortino's more focused, a different lens, Only downside deviation it defends. Treynor takes the beta, throws it in the mix, To judge portfolio gains for each risk unit's fix." Sharpe ratio measures excess return for each unit of total risk (standard deviation). Sortino ratio also measures excess return but only in relation to downside risk. Treynor ratio measures excess return for each unit of systematic risk (beta).

Formulas to Remember

1. Sharpe Ratio = (Portfolio Return - Risk-Free Rate) / Portfolio Standard Deviation 2. Sortino Ratio = (Portfolio Return - Risk-Free Rate) / Downside Deviation 3. Treynor Ratio = (Portfolio Return - Risk-Free Rate) / Portfolio Beta 4. Information Ratio = (Portfolio Return - Benchmark Return) / Tracking Error

Formula Examples

Assume the following data for a portfolio: Portfolio Return: 12% Risk-Free Rate: 2% Portfolio Standard Deviation: 15% Downside Deviation: 10% Portfolio Beta: 1.2 Benchmark Return: 10% Tracking Error: 5% 1. Sharpe Ratio = (12% - 2%) / 15% = 0.67 2. Sortino Ratio = (12% - 2%) / 10% = 1 3. Treynor Ratio = (12% - 2%) / 1.2 = 8.33 4. Information Ratio = (12% - 10%) / 5% = 0.4

Pitfalls to Remember

Comparability:

These ratios are most useful when comparing similar investments or portfolios. Comparing ratios across different asset classes or investment styles may lead to misleading conclusions.