Question

discuss the below table, you must explain (1) what R-Square and Beta measure, and (2) how they are different for each portfolio.

Please explain clearly.

Obs	Portfolio	R-Square	Beta
1	PORT05	0.7598	1.13599
2	PORT10	0.7527	1.21345
3	PORT30	0.8633	1.13248
4	PORT50	0.8991	1.14703
5	PORTmkt	1.0000	1.00000

Answer 1

R-Square measure provides the measure of correlation of the protfolio with the market benchmark. A R-square of 0.75 implies that roughly 75% of the variance in the portfolio can be explained / attributed to the market benchmark.

Beta is the measure of systematic risk (or volatility) of a stock or a portfolio. It measures the sensitivity of the stock to the overall market. Beta of more than 1.0 indicates that the stock or portfolio is more sensitive to market movements. For example, a beta of 1.2 implies that if the stock market moves up/down by 10%, then the stock would move up/down by 12% (10%*1.2). Hence, its volatility is higher than the market.

One key thing to note for an investor while using beta is that the stock should have enough correlation with the market benchmark, only then the beta coefficient will be relevant and useful.

Port05 - It has a high R-square value of 0.7598 and beta greater than 1. It means that the portfolio is significantly correlated to the market and is more volatile than the market.

Port10 - Its R-square value is lower than that of Port05 while beta is higher. This implies that this portfolio is more risky than Port05 but reliability of its beta is lesser than that for Port05.

Port30 - Its R-square value is much higher than those of Port05 and Port10 while beta is lower than both Port05 and Port10. This implies that this portfolio is less risky than Port05 & Port10 with higher reliability of its beta at the same time.

Port50 - Its R-square value is highest among all portfolios, so its beta is the most reliable measure of volatility (or risk).

Overall, all the four portfolios have high correlation to the market and high beta. So, we can reliably presume that these portfolios are more risky than the market. Hence, expected returns should be higher than the expected return of the market, to compensate for the higher risk.