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Stat Ratios - But Why?

An investor should keep in mind that mere returns of a fund are not adequate to make sound

investment decisions as these figures do not reveal the complete story. The end doesntustify the means holds true for investment portfolios as well. This is where the need for

statistical analysis arises. Parameters like Alpha, Beta, R-square, Standard deviation and

Sharpe ratio help an investor to better judge the fund's performance in the true sense. Thesefive indicators account for the risk-return tradeoff associated with the investment in Mutual

funds. Only the historical performance should not be considered while making a future

investment decision. These tools provide the necessary information for investors to evaluatehow effectively their money has been invested.

Risk defined

All investments have inherent risk attributes. Risk refers to the probability of losing money

or failing to make money on an investment. But when the term is specifically used in the

context of Mutual funds, it generally refers to an investor's ability to endure volatility. A fundwith higher risk is usually expected to deliver higher return and vice versa. At the same time,

a long term investment perspective helps investors to suffer relatively lower volatility thanshort term investments.

Interpreting statistical ratios

Alpha:It gauges the fund manager's ability to generate additional returns over the risk-adjusted

returns delivered by the corresponding benchmark index. Investors can get an idea of howmuch value the fund manager through his stock selection ability has added (or eroded) to

(from) the fund. Stock selection could be a combination of sound fundamentals and market

timing. Alpha measures the excess returns generated over a statistically adjusted benchmark

return. A high value for alpha implies that the fund has performed better than what has been

expected.

A positive alpha of 1 means the fund has outperformed its benchmark index by 1%.Similarly, a negative alpha of 1 signifies an underperformance of 1%. The higher the ratio,

the better the risk-adjusted returns.

Alpha = Portfolio Return - Benchmark Portfolio Return;Where:

Benchmark Return = Risk Free Rate of Return + Beta (Return of Market - Risk-Free

Rate of Return)Investors usually judge a fund manager by the return it gives, never by the risk he took toprovide that return. The primary idea behind the concept of Alpha is that the fund manager

should never be analyzed solely on the returns of the portfolio, the risk component associatedwith the investment should also be considered so as to get the correct picture.

Let us take an example of a fund being managed by three fund managers at different times.

Expected portfolio return, Risk-free rate of return and Market return are same for all three

scenarios.

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Fund

Manager

Portfolio

ReturnBeta

Risk-Free rate of

Return

Market

Return

A 20.00% 0.90 5.00% 10.00%

B 20.00% 1.00 5.00% 10.00%

C 20.00% 1.10 5.00% 10.00%

Calculation of Expected Benchmark Return and Alpha

Fund Manager Expected Benchmark Return Alpha

A{0.05 + 0.90 (0.10-0.05)} * 100 =

9.50%20.00% - 9.50% = 10.50%

B{0.05 + 1.00 (0.10-0.05)} * 100 =

10.00%20.00% - 10.00% = 10.00%

C{0.05 + 1.10 (0.10-0.05)} * 100 =

10.50%20.00% - 10.50% = 9.50%

From the above cited example, it is evident that Manager A did best as he generated the

maximum Alpha.

Beta:

Unlike Alpha, which measures the excess returns over the benchmark index, Beta accountsfor the excess risk over the index. It is a measure of the volatility of a portfolio in comparison

to the market as a whole, or more specifically it gauges the tendency of a fund's returns to

respond to the market fluctuations.

If the fund has a beta of 1, it is considered to have the same risk as the overall market. A fund

with a beta greater than 1 is considered to be more volatile than the market and vice versa.Beta of an index is always taken as 1. So by multiplying the beta of a fund with the expectedpercentage movement of an index, the expected movement in the fund can be determined.

Beta is calculated using regression analysis.

Where:

Rp is the Portfolio rate of return

Rm is the Market rate of returnTo illustrate it with an example,

If a fund has a beta of 1.2 and the market is expected to move up by 10%, the fund should

move by 12% (obtained as 1.2 multiplied by 10). Similarly if the market loses 10%, the fundshould lose 12% (obtained as 1.2 multiplied by minus 10).Thus for investors with low risk appetite, investment in stocks / funds with low beta is

preferred. Whereas, investors willing to take higher risk, should invest in high beta stocks /

funds.

However, the problem is that Beta considers past price movements for calculation purpose,

which are poor indicators of future price movements. Hence, Beta can be considered as a

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good measure for short term investors but for investors with long-term horizons, it's less

useful.

R-Squared:

The R-squared value explains the extent to which the beta value is reliable. It measures the

percentage of the funds variations that is attributable to the movements in the benchmarkindex. Values for r-squared ranges from 0 and 1. An R-squared value of 1 indicates that the

fund and the index are perfectly and closely correlated to each other, and the movements ofthe portfolio are entirely explained by the movements in the benchmark, whereas, an R-

squared value of 1 indicates no correlation.

From the above concept of Beta, it is clear that beta is reliant on the index that is used to

calculate it. However, the resulting beta value might not hold any significance if the fund and

the corresponding index is not correlated to each other. Hence, Beta and R-squared must be

used together to judge a funds risk profile.

Where:

X is the Portfolio

Y is the MarketTo cite an example,

An R-squared of 0.7 shows that 70% of the portfolios returns are the outcome of the marketchanges. More specifically, it can be stated that 70% of its profits or losses are due to market

gains. The rest 30% are the consequence of other factors.

Conclusion (The Bottom Line):Besides looking into the funds returns, the investors should also consider the risk associatedwith the investment. The explanation of the above statistical ratios would provide an insight

into the risk adjusted return of the funds under consideration. Without assessing risk-adjusted

returns, an investor cannot figure out the whole investment scenario, which could causeunreliable investment decisions. A high return is not good enough to lure investors; it is

recommendable only if it is not associated with a high risk.