Unit study guide · NISM Series V-D
Mutual Fund Scheme Performance
5 questions in this unit
What this unit covers
- Why is a total-return index generally a more complete benchmark than a price-return index when evaluating an equity fund’s total investment return?
- Over the same annual period, a fund earns 12%, the risk-free rate is 4%, and the fund’s annual standard deviation is 16%. What is its Sharpe ratio? Assumptions: Returns and standard deviation are all on the same annual basis.
- A fund earns 12% over a year when the risk-free rate is 4%, and its beta to the selected benchmark is 0.80. Using Treynor ratio as excess return divided by beta, what is the ratio expressed in percentage points per unit of beta? Assumptions: Beta is defined relative to the stated benchmark and all return inputs use the same year.
- A fund earns 13%. For the same period the risk-free return is 5%, the market benchmark earns 10%, and the fund’s beta is 1.20. Define alpha as actual return minus [risk-free return + beta × (market return − risk-free return)]. What is alpha? Assumptions: The supplied single-period model is used. Inputs are measured over the same period.
- An index fund’s return minus its benchmark return over four equal periods is −1, +1, −1 and +1 percentage points. Use population standard deviation of these differences as tracking error. Which pair is correct? Assumptions: Population standard deviation is used. No annualisation of the four-period measure is requested.
Key ideas
From the practice bank · 1
Why is a total-return index generally a more complete benchmark than a price-return index when evaluating an equity fund’s total investment return?
A total-return index incorporates dividends according to its methodology, commonly through assumed reinvestment. Comparing a fund’s total return only with price changes can leave out part of the benchmark investor’s return. Remember: Compare returns measured on a consistent economic basis.
Hint Consider the cash return earned by an equity holder in addition to price appreciation.
V-D-054From the practice bank · 2
Over the same annual period, a fund earns 12%, the risk-free rate is 4%, and the fund’s annual standard deviation is 16%. What is its Sharpe ratio? Assumptions: Returns and standard deviation are all on the same annual basis.
Sharpe ratio = (12% − 4%)/16% = 0.50. All inputs must use compatible measurement periods and units. Remember: Sharpe ratio relates excess return to total volatility.
Hint Divide return in excess of the risk-free rate by total volatility.
V-D-055From the practice bank · 3
A fund earns 12% over a year when the risk-free rate is 4%, and its beta to the selected benchmark is 0.80. Using Treynor ratio as excess return divided by beta, what is the ratio expressed in percentage points per unit of beta? Assumptions: Beta is defined relative to the stated benchmark and all return inputs use the same year.
Treynor ratio = (12% − 4%)/0.80 = 10 percentage points per unit of beta. Unlike Sharpe ratio, the denominator here measures benchmark-related risk rather than total volatility. Remember: Different risk-adjusted measures use different definitions of risk.
Hint The annual excess return is eight percentage points.
V-D-056From the practice bank · 4
A fund earns 13%. For the same period the risk-free return is 5%, the market benchmark earns 10%, and the fund’s beta is 1.20. Define alpha as actual return minus [risk-free return + beta × (market return − risk-free return)]. What is alpha? Assumptions: The supplied single-period model is used. Inputs are measured over the same period.
The model benchmark is 5% + 1.20 × (10% − 5%) = 11%. Alpha is 13% − 11% = +2 percentage points under this model and these inputs. Remember: Alpha depends on the specified risk model and benchmark.
Hint Calculate the beta-adjusted required return before comparing it with 13%.
V-D-057From the practice bank · 5
An index fund’s return minus its benchmark return over four equal periods is −1, +1, −1 and +1 percentage points. Use population standard deviation of these differences as tracking error. Which pair is correct? Assumptions: Population standard deviation is used. No annualisation of the four-period measure is requested.
The four differences sum to zero, so their mean is zero. Each squared deviation from zero is one, making population tracking error sqrt(1) = 1 percentage point. Remember: A fund can have no average tracking difference and still have non-zero tracking error.
Hint Calculate the average difference, then the variability around that average.
V-D-058