Question

1. A risk-free security is one with no uncertainty in its future payoffs. Hence, there is no volatility, and so the variance of its return is 0. According to the CAPM, is it possible that a security with a positive variance can have a required return that is less than the risk free rate? If so, explain what characteristics this asset needs to have and why this would mean an investor would accept a return less than the risk free rate when there is uncertainty in the asset’s future payoffs.

Answer 1

So first, let us look at the CAPM model

The CAPM model is used to determine the cost of equity (Ke) for a particular security.

According to the CAPM model, Ke = Rf + B*( Rp - Rf)

Where Ke = cost of equity

Rf = Risk free Rate

B = Beta

Rp = Market average returns

Now for the question, yes it is possible that a stock which has positive variance can give returns below the risk free rate, If the security in question has a Negative Beta.

For eg: Consider a company XYZ, their business is to help companies deal with bankruptcy. Now when the economy is running smoothly, the number of companies going bankrupt will be lower, and hence company XYZ will have low revenues when the economy is doing well.

But when the economy is doing badly (as it is right now, due to covid), A lot more companies are filing for bankruptcies and hence Company XYZ is doing good.

So when the economy does well, XYZ underperforms and vice- versa, hence it has a negative beta.

An investor would still want to invest in this stock for the purpose of Diversification.

Diversification balances out an investors portfolio so that he is ensured steady returns despite the performance of the economy