Question

the standard deviation of the portfolio's return is lower than those of the two securities, A and B. What is the intuition behind this? Is it always the case? Examine how the returns on these two securities behave. Do they move together or in opposite directions?

Meaning of the Beta

If there is a security with a negative beta, for example -0.5, what can you say about the expected return of the security based on the Capital Asset Pricing Model (CAPM), or the Security Market Line (SML)? Would it be greater or smaller than the risk-free interest rate? How can you explain your answer intuitively?

Answer 1

As per the Modern Portfolio theory:

Whenever we combine securities in a portfolio:

Expected return of the portfolio E(Rp): weighted average of the returns of individual stocks.

Standard deviation of the portfolio

is less than (OR)

Equal to:

Weighted average of standard deviations of individual stocks.

In other words risk gets reduced in a portfolio,we called is benefit of diversification that is risk reduction.

When coefficient of correlation (r) =+1, between two stocks then there is no benefit of diversification.

In other words:

the standard deviation of the portfolio's return IS EQUAL TO those of two securities, A and B.

SO IT IS NOT ALWAYS THE CASE.

when r=+1

It means two stocks behave exactly the same in terms of return and volatility.

If A increase by 15%, then B also increase by 15%

Both A and B move together and in the same direction.

Meaning of beta:

Interpretation:

B is the sensitivity of stock return to market return.

Thus if B of a stock=2, it means that when the market changes by 1% stock return is expected to change on an average by 2% in the same direction.

"Since all stocks are directly related to the economy BETA CANNOT BE NEGATIVE."

Of course exams are great and beta may be negative in the sums.

If we get negative beta in a stock.

Since beta is negative the stock should be held in the portfolio to act as a hedge against market risk.

That is if the market falls, all the stocks will fall, but the stock whose beta is negative will rise and save us.

Theoretical speaking: if security has negative beta.

The expected return of the security is smaller than risk free interest rate if market rises.

In fact it has a negative return.

It means if market rises; stock will give a negative return.

If market falls the the expected return on the security is greater than risk free rate.

As stock has a positive return.

And Risk free rate is Negative or near to zero.

Thank you. Hope you find it helpful.