Question

-Assume all unrealistic assumptions related to CAPM holds. Still the assumption which says “all investors will buy market portfolio” seems to be unrealistic.

-Standard deviation and beta (beta is for stocks) both measure the same concept.

-Ignoring the magnitudes, Correlation is still more accurate than Covariance.

This is true or false, so a brief explanation would be very helpful, Thanks!

Answer 1

Market portfolio is a portfolio consisting of weighted assets of the market assuming that these assets can be divisible. Through CAPM has many assumptions, if we look at this one, we should understand that not all investors have good borrowing capacity to be able to invest in a market portfolio so as to manage their risk. Thus, the assumption which says "all investors will buy market portfolio" seems to be unrealistic.

The statement is true.

Beta measures the risk of market whereas standard deviation measures the risk of individual stocks. To be specific to the understanding relating to stock, beta measures the volatility of a stock in relation to the market trend whereas standard deviation considers historical reports and is a measure of volatility of the stock over a period of time. When one has to make an investment it is advisable to look at the beta than the historical data provided by standard deviation.

So, we see that standard deviation and beta for stocks measure different concepts.

The statement given is False.

Both correlation and covariance measure the linear dependency between two variables. However, of the two, covariance is not standardised. It can take any value between -infinity to infinity. This makes comparison difficult. Also, covariance is not scale invariant, meaning that a change in unit of variable brings about a change in the covariance too. It cannot be used as an absolute measure of dependence as it depends on the measurement scale.

Correlation on the other hand, ranges between -1 to +1 making the comparison between two variables an easy job. Comparing the degree of dependency or association between two random variables becomes easy.

Thus it is true that Correlation is more accurate than Covariance.