Question

There are two tasks in portfolio choice problem:

(i) determination of the optimal risky portfolio and (ii) capital allocation.

These two tasks are independent, or one is separate from the other. Explain why

Answer 1

A portfolio choice depends on the risk-return profile of the investor. A highly risk-averse investor would want to invest more of his capital in risk-free assets while a less risk-averse investor would want more proportion of capital in risky-assets.

In this case, the first task is always to find the optimal risky portfolio. This is done by taking into account the expected returns on the individual assets as well as the standard deviation or volatility that these stocks are likely to show. The optimal risky portfolio is determined by mapping out all possible securities with different asset weight allocations. If we plot this on a graph (also known as efficient frontier), we would plot Standard deviation vs Expected returns of the risky portfolio, which typically would show that as risk (measured in terms of volatility or standard deviation) increases, the expected returns from the optimal risky portfolio also increases. This task is concerned with providing the investors with the best optimal risky investment portfolio. This portfolio is the same for all the investors, irrespective of their risk profile.

On the other hand, capital allocation is a totally different task and this is determined basis the risk profile of the investor. Since subjectivity and the choice of the investor come into the picture, the capital allocation is a personal choice of the investor.  The investor chooses how much proportion of his capital does he want to invest in a risky portfolio and how much in risk-free assets. The capital allocation line is a line on a graph depicting all possible combinations of risk-free assets and risky assets. The slope of the capital allocation line is the Sharpe ratio. An investor who wishes to take on more risk has a capital allocation line with a higher slope and vice-versa.

After both these independent tasks are carried out, the optimal portfolio s found at the point where the capital allocation line is just tangent to the efficient frontier. Any less or high risk-averse investor would prefer a different capital allocation and hence would have a different portfolio of risky and risk-free assets.