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Portfolio Management

Module Units

# Portfolio Return

To put it simply, portfolio return is the gain or loss realized from the invested amount. The main objective of a portfolio is to generate returns.

### How is it measured?

The expected return of a portfolio is measured by the weighted average of the expected return of individual assets (for example, shares, commodities) etc. The weights are the individual proportion of the individual assets in the portfolio, with the total portfolio weight being 100.

### Portfolio return formula:

Rp = ∑ (Wi X Ri)

Where:

R = Expected return of a portfolio
P = Proportion or weights of total funds invested in security i
i = Security/Asset
Wi = Weight of security i in the portfolio
Ri = Individual return of security i

Example of portfolio return calculation:

Let us assume that there is a portfolio with a total investment of ₹ 100,000 consisting shares of 3 different companies. The details are given below:

Portfolio Return Formula = (12% X 50%) + (8% X 20%) + (10% X 30%)

Portfolio Return = 10.6%

The main purpose of calculating portfolio return is to evaluate our performance against a predetermined benchmark that is suited according to the risk undertaken by the investor. For example, if the investor’s portfolio primarily comprises blue-chip stocks, the Nifty 50 index would be an appropriate benchmark. Likewise, if the investor holds a globally diversified portfolio, the MSCI World Index would be a suitable barometer for measuring the investor’s return.

This is why you will often hear terms like “X portfolio outperformed the Sensex by 2%” which means that the returns of that portfolio in a given period is 2% more than the returns obtained by Sensex.

### Portfolio Alpha

We mentioned before that return of a portfolio is usually measured against a benchmark. This measure is known as Alpha. In other words, the difference between the return of a portfolio and the benchmark is known as Alpha. A positive alpha of +4 means that the portfolio has outperformed the benchmark by 4%. A negative alpha of -4 means that the portfolio has underperformed the benchmark by 4%. An alpha of zero (0) means that the portfolio’s return is the same as the benchmark’s return.

### Portfolio Alpha calculation

Alpha = R – Rf – beta (Rm-Rf)

Where:

R represents the portfolio return
Rf represents the risk-free rate of return
Beta represents the systematic risk of a portfolio
Rm represents the market return, as per a benchmark

### Example of portfolio alpha calculation:

Let us continue with our previous example.

The portfolio return (R) is 10.6%

Let us assume risk-free rate of return (Rf) is 2%

The benchmark’s return (Rm) is 9%

The beta of the portfolio (Rm-Rf) is 7%

The portfolio alpha is

Alpha = R – Rf – beta (Rm-Rf) = 1.6%

Remember, the key is to obtain a higher risk-adjusted return and not total returns.

In terms of portfolio diversification, portfolio return plays a major role. The portfolio manager aims to choose assets in such a way that the performance of one is offset by the performance of another.

In our above example, if we consider asset 2 is a bond and its yield falls from 8% to 6%, the overall return of the portfolio will fall to 10.2%. Hence, instead of suffering a loss of 2%, the investor loses only 0.4%, since the drop in the return is offset by the return from asset 1 and asset 3.

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Units 7/16