Measures for Security and Portfolio Analysis
A few measures for security and portfolio analysis are as follows:
- Alpha
- Beta
- Sharpe ratio
- Treynor ratio
Alpha
Alpha measures risks against returns and tells whether a particular fund has produced returns justifying the risks that it is taking. This is done by comparing two figures - the actual return and the return predicted by beta.
Alpha is a measure of selection risk [also called residual risk] of a security in relation to the market. A positive alpha is the extra return awarded to the investor for taking additional risk rather than accepting the market return.
Alpha can also be viewed as a measure of fund manager's performance - the amount arrived at is what the fund has earned over and above [or under] what it was expected to earn, indicating the value added [or subtracted] by the fund manager's investment decisions.
Passive funds, like index funds, that track a benchmark index always have or should have an alpha of 0. Incase of active funds, the alpha is a measure of what the fund manager's activity has contributed to the fund's returns.
The formula for alpha is given below -
[(sum of y) - (b (sum of x))] / n
Where:
n = number of observations
b = beta of the fund
x = rate of return of the market
y = rate of return of the fund
A positive alpha indicates that the fund has performed better than expected while a negative alpha indicates that the fund or portfolio has underperformed at the same level of risk.
Beta
Beta is the measure of volatility or change in price of a security with respect to the market or the benchmark. It represents the correlation between the return on an instrument versus the return of the market. It measures a security's market risk and shows a security's volatility in relation to the market. Beta indicates how risky a security is if the security is held in a well-diversified portfolio.
Incase of a mutual fund scheme, beta can be calculated as - percentage change in NAV of the portfolio / percentage change in Benchmark Index
In order for the beta to be effective, there should be a correlation between the index used and the fund. Incase the index bears no relation with the movements in the fund, for instance, if the beta is calculated for a large-cap fund against a mid-cap index, the resulting value will have no meaning since the movement of the fund will not be in tandem with the index.
Beta has its own limitations. Beta is only a historic tool which does not incorporate new information. Since beta relies on past movements, it cannot be used for new stocks that have insufficient price history for establishing a reliable data. Finally, beta is just an indication. It depends on past price movements that cannot be a appropriate predictors of future movements.
Sharpe Ratio
The performance of a portfolio must be considered with respect to the risk assumed. There exists downside risk of investing and high returns are associated with high degree of volatility. Sharpe ratio assesses the return generated by a portfolio, per unit of risk undertaken. Here, the risk is taken to be the portfolio's standard deviation which is indicative of the volatility in the returns of a security. A lower standard deviation implies a small amount of fluctuation in the returns.
Mathematically, this ratio is the difference between the portfolio's returns over the return earned on a risk free investment divided by the standard deviation of the portfolio, given below -
(Return of portfolio - Risk-free rate of return) / Standard deviation of the portfolio
Thus, a higher Sharpe ratio is better since it represents a higher return generated per unit of risk. Sharpe ration can only be used as a comparative tool and has no meaning in isolation.
Treynor Ratio
Treynor ratio is another ratio like Sharpe ratio that measures the returns earned per unit of risk taken. However, the difference is that Treynor ratio uses the portfolio beta as the benchmark unlike the standard deviation used by Sharpe ratio. Treynor ratio is calculated as follows -
Treynor ratio = (Return of the fund - Risk free return) / Portfolio beta
The higher the ratio, better is the performance.
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