Risk-adjusted returns are the calculative returns your funds make compared to the risk indicated over the period of time. Relative returns cannot be used alone to evaluate the performance of mutual funds, as it does not indicate the risk taken by the fund manager. It would be unfair to the fund manager who has taken more risk and has generated returns equal to that of its peers. So if compared, a couple of mutual funds which drive the same percentage of returns over the same period of time, the lesser risk funds have a higher Risk-Adjusted Returns. There are various measures of risk-adjusted returns.

  1. Sharpe ratio

Sharpe ratio refers to the excess return that the scheme earns than the risk-free rate of return, for per unit of risk taken. The risk-free rate of return is the return that can be earned by investing in government securities. The return based on a Treasury bill index is often used for the purpose. Sharpe Ratio uses Standard Deviation as a measure of risk.

Risk Premium = Return earned on scheme (Rs) – Risk-free Return (Rf)

Sharpe Ratio = Risk Premium / Standard Deviation of the scheme

=               ( Rs – Rf)/  Standard deviation of the scheme

Example: If the risk-free return is 5%, and a scheme with a standard deviation of 0.5 earned a return of 7%, its Sharpe Ratio would be (7% – 5%) ÷ 0.5 i.e. 4%.

Sharpe ratios can be compared with other Sharpe ratios for other schemes of the same type. Higher the Sharpe Ratio, better the scheme is considered to be.

  1. Treynor ratio

Treynor ratio also measures the excess return earned by the scheme with compared to the risk-free rate of return. The difference between the Treynor ratio and Sharpe ratio is that of the measure of risk chosen. Treynor ratio uses Beta as a measure of risk.

Treynor Ratio     =               (Rs – Rf)/  Beta of the scheme

=                (Rs – Rf)/  Β

Example: if risk free return is 5%, and a scheme with Beta of 1.2 earned a return of 8%, its Treynor Ratio would be (8% – 5%) ÷ 1.2 i.e. 2.5%.

Higher the Treynor Ratio, better the scheme is considered to be. Since the concept of Beta is more relevant for diversified equity schemes, so it would be more appropriate if used for diversified equity portfolios.

  1. Jensen’s alpha

This is a measure of out-performance. It compares the actual scheme performance, with what it ought to have been, given the risk in the scheme. Alpha measures the difference between a fund’s actual returns and its expected performance, given its level of risk.

Jensen’s Alpha = {(Fund return-Risk free return) – (Funds beta) *(Benchmark return- risk free return)}.

Example: Fund return 10%; Risk free return 8%; Benchmark return 5%; Beta of Fund 0.8

By computing with above formula we will get alpha as 4.4 for this fund

A positive alpha means the fund has outperformed its benchmark index. Correspondingly, a negative alpha would indicate an underperformance. Investors are often advised to pick funds with high Jensen Alpha ratios. This should be ideally used to evaluate diversified equity portfolios.

  1. Appraisal ratio

It is a ratio used to measure the quality of a fund’s investment-picking ability. It compares the fund’s alpha to the portfolio’s unsystematic risk. The appraisal ratio adjusts Jensen’s α for unsystematic risk through the equation:

The smaller the unsystematic risk, the better the results the fund has established as measured by the appraisal ratio. Or higher the ratio, better is the scheme.

  1. Sortino Ratio

This ratio measures the performance of the scheme relative to the downside deviation. Standard deviation involves both the upward as well as the downward volatility. Since investors are only concerned about the downward volatility, Sortino ratio presents a more realistic picture of the downside risk of the fund.

Sortino Ratio = (Scheme Return – Risk-free Return)/  Downside Deviation

Higher Sortino Ratio means that the scheme offers a better return per unit of risk. Or a high Sortino ratio indicates that there is a low probability of a large loss.

  1. Eugene Fama

It is just like Jensen Alpha, with standard deviation as the measure of risk. It measures out-performance by comparing the actual scheme returns, with the returns that ought to have been earned, given the standard deviation risk.

The return that ought to have been earned can be taken to be equal to

Risk-Free Return + {(Standard Deviation of Scheme ÷ Standard Deviation of Market) X (Market Return – Risk-Free Return)}

This return would be then subtracted from the return actually earned by the scheme.

Example: Rf=7%; Standard Deviation of Scheme=4.7%; Standard Deviation of Market=2.62%; Market Return=11.42%; Scheme return=29.47%

Return ought to be earned= 7%+ {(4.70% ÷ 2.62%) X (11.42% – 7%)} i.e. 14.92%.

The scheme return was 29.47%.

The Eugene Fama is 29.47% – 14.92% i.e. 14.55%.

The positive number indicates out-performance.

Higher the positive number, better the scheme and it can be used for all schemes.

  1. Modigliani & Modigliani (M2)

Modigliani-Modigliani or M-squared return is the hypothetical return an investor would have earned in a time frame had the fund’s risk been adjusted to match that of a benchmark. This measure equals the returns the fund would have received, had it borne the same risk the market index had. However, the results can be misleading if a mutual fund has changed its investment style or strategy. Again, whether the returns can be sustained in future is doubtful.

The M2 value is given by the formula:

Risk-Free Return + {(Scheme Return – Risk-Free Return) X (Standard Deviation of Market ÷ Standard Deviation of Scheme)}

If the M2 value is higher than the market return then it can be said that the scheme has done better than the market.


CMT Level 1 Study Material

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