What is MPT Statistics and what are it's measures?

What is MPT Statistics and what are it's measures?

The modern portfolio theory (MPT) is a practical method for selecting investments to maximize their overall returns within an acceptable level of risk. MPT stresses the importance of diversification.

Generally, A high return stock is subject to higher risk, whereas a low return stock is subject to lower risk. MPT argues that an investor must construct a portfolio of multiple classes of assets that is capable of generating higher returns with acceptable risk. Therefore, the mixture of higher return stocks & lower return stocks can result in an optimal situation, and that is how you can maximize your return with minimal risk. 

In the portfolio analyzer report, MPT statistics consists of 5 measures:

  1. Alpha

  2. Beta

  3. R Squared

  4. Tracking Error

  5. Information Ratio


Alpha measures a stock’s performance after adjusting for the stock’s systematic risk as measured by the stock’s beta with respect to the index. A positive Alpha indicates good performance & a negative Alpha indicates not so good performance. 

Alpha = Actual Returns - Benchmark Index Returns

For Instance, HDFC bank has a yearly return of 15%, and the annual return of the Nifty50 Index is 12%. So, the Alpha of HDFC Bank will be 3% (15% - 12%). A positive alpha of 3% means that HDFC bank has outperformed the Nifty50 Index.


Beta is a measure of a stock’s volatility to movements in the index. Each stock has its own beta, and the volatility is compared to the benchmark index. 

Let’s say the beta of Nifty50 is 1.00, and the beta of GAIL (Stock) is 1.20. If the nifty value increases by 2%, GAIL’s price will increase by 2.4%(1.20*2%). So, the higher the beta of GAIL, the higher will be its excessive return over the Nifty50 index and vice-versa.

As per the image displayed above, the portfolio beta based on the last 3 and 5 years is 1.42 and 1.43, respectively, which is relatively high. Therefore, the investor can look at investment opportunities with lesser beta instruments.

R Squared:

R-Squared measures how closely the performance of a stock can be attributed to the performance of a benchmark index. It is measured on a scale between 0 and 1; 0 means that there is no correlation between the stock and the benchmark index, and 1 means that the portfolio and the benchmark index are perfectly correlated. 

R-Squared of less than 0.50 doesn’t mean bad. It just means the correlation between the portfolio and the selected benchmark index is less.

In the portfolio analyzer, the R-Squared of the portfolio is measured with the large-cap funds.

In the image displayed above, the R-Squared of the portfolio holdings is 0.58 or 58% which means the client's portfolio is moderately correlated with the large-cap funds.

Tracking Error:

It is a measure of financial performance that determines the difference between the return fluctuations of an investment portfolio & a chosen benchmark Index.

Generally, portfolio risk is measured against a benchmark. So, tracking error is commonly used to ascertain how well the investment performs. A high tracking error means that the portfolio returns are subject to more volatility, and the portfolio is not consistent in exceeding its benchmark returns.

0% Tracking error means the portfolio is optimal in relation to its Benchmark index. Most fund managers would go for investments with a tracking error between 1%-15%, depending on their risk appetite. However, beyond 15%, the investment is inconsistent and risky.

As per the image displayed above, the portfolio's tracking error based on the last 3 and 5 years is 26.04% and 23.22%, respectively, which is high. Therefore, the investor needs to look at different instruments for investment and look to reduce the Tracking error.

Information Ratio:

Information Ratio (IR) measures portfolio returns above a benchmark index's returns to the volatility of those returns.

It is calculated using Benchmark return and Tracking error:
Information Ratio = (Portfolio Returns - Benchmark Returns)/Tracking error

The Information ratio can test the consistency of an investor as it determines whether he has beaten the benchmark by a large margin in a few months or by small margins every month.

For a given level of risk taken, a higher active return will result in a higher Information ratio, which in turn proves the consistency of the investor in delivering superior returns.

A portfolio with an information ratio of less than 0.4 is considered to be a bad investment whereas an IR between 0.4 and 0.6 is said to be a good investment. However, an IR of greater than 0.6 is considered a great investment. A negative information ratio means the investment has failed to perform.

For Instance, Ms. Pooja, a client of FYERS, has a portfolio return of 20% with a tracking error of 4%. The Benchmark index is 16%. The Information ratio of Pooja is  1 {(20-16)/4} which means Pooja has made a great investment. 

As per the image above, The information ratio of the portfolio based on the last 3 and 5 years is -0.59 and -0.57, respectively, which is negative. The investor needs to re-evaluate his portfolio holdings as they look like a good investment.