# Computation of returns from Mutual Funds

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Mutual Fund are funds wherein investor invests money and owns part of assets owned by mutual fund that corresponds to his/her share in the fund. Besides return on buying and selling of the Mutual Fund units hold by investor, an investor derives three types of income from owning such mutual fund units.

• Cash Dividend
• Capital Gains Disbursements
• Change in the fund’s Net Asset Value (NAV) per unit (Unrealised Capital Gains)

For an investor who holds a mutual fund for say 1 year, the one-year holding period return is given by

Return = Dividend + Realised Capital Gains + Unrealised Capital Gains/Base Net Asset Value

I.e., R = D1 + CG1 + (NAV1 – NAV0) / NAV0 x 100

Where,

D1 = Dividend

CG1 = Realised Capital Gains

NAV1 – NAV0 = Unrealised Capital Gains

NAV0 = Base Net Asset Value

Illustration 1

A mutual fund, that had a net asset value of ₹10 at the beginning of the month, made income and capital gain distribution of ₹0.15 and ₹0.04per unit respectively during the month and then ended the month with a net asset value of ₹10.15. Compute the monthly return.

Here, D1 = 0.15, CG1 = 0.04, Unrealised Capital Gains =NAV1 – NAV0 = 10.15 – 10.00 = ₹0.15

Monthly Return = (0.15 + 0.04 + 0.15)/10 x 100 = 3.4%

Illustration 2

A mutual fund raised ₹200 lakhs on April 1, by issue of 20 lakh units at ₹10 per unit. It used ₹190 lakhs to invest in several capital market instruments. Its initial expenses were ₹8 lakhs and during the month of April, it sold certain securities costing ₹60 lakhs for ₹90 lakhs. It also purchased in same month, other securities for ₹70 lakhs. Expenses for fund manager was ₹10 lakhs of which ₹1 lakh is in arrears. 80% of the realised earnings were distributed. Dividend earned was ₹6 lakhs. The Market value of the investment hold by mutual fund on 30th April was ₹180 lakhs.

Now suppose, an investor subscribed to 1 unit on April 1 and disposed it off at closing NAV on 30th April. What will his annual rate of earning.

Here, lets calculate closing NAV first,

 Amount in ₹ lakhs Amount in ₹ lakhs Amount in ₹ lakhs Opening Bank (200-190-8) (initial receipts – investment made – expenses pertaining to initial receipts) 2 Add: Proceeds from sale of securities 90 Add: Dividend received 6 98 Cost of securities purchased 60 Fund Management Expenses paid (10-1) 9 Capital gain distributed = 80% of (90-60) 24 Dividend Distributed = 90% of 6 4.8 97.8 Closing Bank .2 Closing Market value of investments 180 180.2 Less: Arears of Expenses 1 Closing Net Assets 179.2 Number of Units (Lakhs) 20 Closing NAV per unit 8.96

Now, let’s calculate rate of earning,

 Amount Income received (24 + 4.8)/20 1.44 Loss: Loss on disposal (10 – 8.96) 1.04 Net Earning 0.4 Initial Investment 10 Rate of earning monthly 4% Rate if earning (Annual) 48%

A better way to describe performance of mutual fund return can be described from following three sources –

• Dividend Earned
• Capital Gain Distribution/Earned
• Change in price or NAV

In case investment is held for a period less than 1 year, then pay offs can be easily converted into returns by using Holding Period Return (HPR) formula, which is as follows – In order to assess the performance of Mutual Funds, often ratios are used. Sharpe Ratio and Treynor Ratio are two of such ratios. Both Sharpe Ratio and Treynor ratio measure risk adjusted returns. While Sharpe ratio measures total risk (as the degree of volatility in returns captures all elements of risk – systematic as well as unsystemic), the Treynor ratio captures only systematic risk in its computation. It is therefore, when one has to evaluate the funds which are sector specific, Sharpe ratio would be more meaningful. This is due to the fact that unsystematic risk would be present in sector specific funds. Hence, a truer measure of evaluation would be to judge the returns based on the total risk. On the contrary, if we consider diversified equity funds, the element of unsystematic risk would be very negligible as these funds are expected to be well diversified by virtue of their nature. Hence, Treynor ratio would be more apt here. However, usually both ratios give similar rankings. Jensen’s Alpha and Expense Ratio are other two such ratios that are used to analyse performance of the mutual fund.