Measures of Returns
This sub‑topic covers the various ways to measure the returns generated by mutual fund investments. Understanding these measures helps you compare schemes, answer exam questions on performance, and advise clients accurately. The content links directly to the Risk, Return and Performance chapter and is essential for NISM Series V‑A certification.
Learning Objectives
- 1Define and calculate Holding Period Return (HPR).
- 2Convert HPR to an annualised figure using the appropriate formula.
- 3Explain Compound Annual Growth Rate (CAGR) and differentiate it from simple averages.
- 4Identify the difference between arithmetic and geometric average returns and when each is used.
Classification of Return Measures
Absolute return is the simple difference between the ending and beginning value of an investment, ignoring the time factor. It is useful for a quick snapshot but does not allow comparison across different holding periods.
Holding Period Return (HPR) incorporates any cash flows such as dividends or capital gains distributions received during the holding period. By expressing the gain as a proportion of the initial investment, HPR provides a more realistic picture of performance.
For the NISM exam, you will often be asked to convert HPR into an annualised return so that schemes with different tenures can be compared on a like‑for‑like basis. Remember that the exam expects you to use the exact formula given in the syllabus, not a shortcut.
- HPR is a period‑specific measure.
- Annualised return standardises the period to one year.
Many candidates mistakenly treat the raw HPR as the yearly return. Always annualise the HPR using the (1+HPR)^{1/n}‑1 formula before comparing with other funds.
Holding Period Return (HPR)
HPR measures the total return earned over the exact period an investor holds a mutual fund unit, including price appreciation and any interim cash distributions. The formula captures the effect of dividends, interest, or capital gains that are paid out during the holding period.
Mathematically, HPR is expressed as the ratio of the net gain (ending value plus cash flows minus beginning value) to the beginning value. The result is a decimal that can be multiplied by 100 to obtain a percentage.
In the NISM exam, you may be given the beginning NAV, ending NAV, and the amount of dividend per unit. Plug those numbers into the HPR formula and then, if required, annualise the result.
Where:
V_{f}= Ending value or NAV at the end of the holding period (in rupees)V_{i}= Beginning value or NAV at the start of the holding period (in rupees)D= Total cash distributions received during the period (dividends, interest) per unit (in rupees)Worked Example
Given V_i = 1000, V_f = 1150, D = 50: Step 1: HPR = (1150 - 1000 + 50) / 1000 Step 2: HPR = 200 / 1000 = 0.20 Verification: (1150 - 1000 + 50) / 1000 = 0.20.
Annualising the Holding Period Return
Investors and exam takers need a common time‑basis to compare funds that have different investment horizons. Annualising converts a multi‑year HPR into an equivalent one‑year return, assuming compounding over the period.
The standard annualisation formula is (1 + HPR)^{1/n} - 1, where n is the number of years (or fractions of a year) the investment was held. This method respects the geometric nature of returns, unlike a simple division by n.
On the exam, you will often see a question that provides a 2‑year HPR and asks for the annualised return. Remember to first add 1 to the HPR, raise to the power of 1/n, then subtract 1.
Where:
HPR= Holding Period Return expressed as a decimaln= Holding period in years (or fraction of a year)Worked Example
Given HPR = 0.20 for a 2‑year holding period: Step 1: Annualised = (1 + 0.20)^{1/2} - 1 Step 2: Annualised = (1.20)^{0.5} - 1 ≈ 1.0954 - 1 = 0.0954 Verification: (1 + 0.20)^{1/2} - 1 = 0.0954 (≈9.54%).
Compound Annual Growth Rate (CAGR)
CAGR is the most frequently asked return measure in the NISM exam. It represents the constant annual growth rate that would take an investment from its beginning value to its ending value over a specified number of years, assuming compounding.
The formula is similar to the annualised return formula but uses the ratio of ending to beginning value directly, without adding interim cash flows. This is appropriate when cash flows are reinvested or when you are analysing total asset growth.
When a question provides the initial NAV, final NAV, and the number of years, compute CAGR and compare it with other schemes' CAGR to identify the better performer.
Where:
V_{f}= Ending value or NAV (rupees)V_{i}= Beginning value or NAV (rupees)n= Number of years the investment was heldWorked Example
Given V_i = 1000, V_f = 1500, n = 3 years: Step 1: CAGR = (1500 / 1000)^{1/3} - 1 Step 2: CAGR = (1.5)^{0.3333} - 1 ≈ 1.1447 - 1 = 0.1447 Verification: (1500/1000)^{1/3} - 1 = 0.1447 (≈14.47%).
Average Returns – Arithmetic vs Geometric
The arithmetic average return adds up the periodic returns and divides by the number of periods. It is easy to compute but can overstate performance when returns are volatile because it ignores compounding.
The geometric average return (also called the compounded annual growth rate for equal periods) multiplies the growth factors (1+R_i) together, takes the nth root, and subtracts 1. This measure respects the effect of compounding and is the figure the NISM exam expects when asked for "average annual return" over multiple years.
Common exam mistake: using the arithmetic mean for multi‑year returns. Always check the wording – if the question mentions "average annual return" over several years, use the geometric method.
Key Differences between Arithmetic and Geometric Average Returns
| Aspect | Arithmetic Average | Geometric Average |
|---|---|---|
| Computation | ΣR_i ÷ n | (∏(1+R_i))^{1/n} - 1 |
| Effect of Volatility | Overstates when returns vary | Accurately reflects compounding |
| Typical Use in Exams | Short‑term single‑period analysis | Multi‑year performance comparison |
If all yearly returns are identical, arithmetic and geometric averages are equal. Otherwise, geometric ≤ arithmetic. This rule helps you spot unrealistic answer choices.
Money‑Weighted vs Time‑Weighted Returns (Qualitative)
Money‑Weighted Return (MWR) treats the investor's cash flows as part of the performance calculation. It is essentially the internal rate of return (IRR) of the cash‑flow series and is useful when the investor makes irregular contributions or withdrawals.
Time‑Weighted Return (TWR) eliminates the impact of cash flows by measuring the growth of each sub‑period and then compounding them. TWR is the preferred metric for comparing fund managers because it reflects only the manager’s investment decisions.
For NISM, you are rarely required to compute MWR or TWR numerically, but you should be able to identify which measure is appropriate in a given scenario and explain the rationale.
Risk‑Adjusted Return – Sharpe Ratio (Formula)
The Sharpe Ratio evaluates how much excess return a fund generates per unit of risk (standard deviation). A higher Sharpe indicates better risk‑adjusted performance.
In the Indian context, the risk‑free rate is often taken as the yield on a 10‑year government bond. The exam may provide the portfolio’s average return, the risk‑free rate, and the standard deviation, asking you to compute the Sharpe.
Remember that the Sharpe Ratio is unit‑less; you can compare funds across asset classes only if the same risk‑free benchmark is used.
Where:
R_{p}= Average portfolio return (in percent per annum)R_{f}= Risk‑free rate (in percent per annum)\sigma_{p}= Standard deviation of portfolio returns (in percent per annum)Worked Example
Given R_p = 12%, R_f = 6%, σ_p = 10%: Step 1: Sharpe = (12 - 6) / 10 Step 2: Sharpe = 6 / 10 = 0.60 Verification: (12 - 6) / 10 = 0.60.
Annualised Returns of Three Mutual Funds (5‑Year Horizon)
Scenario
An investor purchases units of a balanced fund at a NAV of Rs. 950. After 18 months, the NAV rises to Rs. 1,080 and the fund has paid a dividend of Rs. 30 per unit during the holding period. Compute the Holding Period Return and convert it to an annualised return.
Solution
Step 1: Identify values – V_i = 950, V_f = 1,080, D = 30, holding period = 1.5 years.\nStep 2: HPR = (1,080 - 950 + 30) / 950 = (160) / 950 ≈ 0.1684 or 16.84%.\nStep 3: Annualised Return = (1 + 0.1684)^{1/1.5} - 1. Compute 1.1684^{0.6667} ≈ 1.1089. Subtract 1 gives 0.1089 or 10.89%.\nStep 4: Round to two decimals – HPR = 16.84%, Annualised Return = 10.89%.
Conclusion
The investor earned a 16.84% return over 18 months, which translates to an annualised return of about 10.9%. Knowing how to move from HPR to an annual figure is a common NISM exam requirement.
⭐Exam Takeaways
- Holding Period Return (HPR) = (Ending NAV – Beginning NAV + Distributions) ÷ Beginning NAV.
- Annualised Return = (1 + HPR)^{1/n} – 1, where n is the holding period in years.
- CAGR = (Ending NAV ÷ Beginning NAV)^{1/n} – 1 and is the preferred "average annual return" for multi‑year horizons.
- Use geometric average (compounded) for multi‑year returns; arithmetic average can overstate performance.
- Money‑Weighted Return reflects cash‑flow timing; Time‑Weighted Return isolates manager skill.
- Sharpe Ratio = (Portfolio Return – Risk‑free Rate) ÷ Standard Deviation; higher values indicate better risk‑adjusted performance.
- Never treat raw HPR as a yearly return – always annualise before comparison.
- In tables or charts, ensure percentages add up logically; the exam often tests interpretation of such visuals.
Practice Questions
8 questions on Measures of Returns
Holding Period Return (HPR) is calculated as
Which formula converts a multi‑year HPR into an annualised return?
An investment has a beginning NAV of Rs.1000, an ending NAV of Rs.1150 and received a dividend of Rs.50 per unit. What is the HPR?
If the HPR for a 2‑year holding period is 0.20, what is the annualised return?
A fund posted yearly returns of 10%, -5% and 15% over three years. What is the geometric average return?
When an investor makes irregular contributions and withdrawals, which return measure best reflects the timing of those cash flows?
Given a portfolio return of 12% per annum, a risk‑free rate of 6% and a standard deviation of 10%, what is the Sharpe Ratio?
Which of the following is a common exam trap regarding Holding Period Return?