Question

(b) If a portfolio has a beta equal to 1, it is an efficient portfolio and it sits on the CML. Is
this statement true or false? Explain.

(c) In practice, it is estimated that most unsystematic risk can be diversified away in a
portfolio of 20 to 30 assets. Is this statement true or false? Explain.

(d) Define idiosyncratic risk and systematic risk. Discuss their relationship with risk
premium and beta.

Answer 1

b) A beta of 1 does not make a portfolio efficient. It simply means that the systematic part of the risk is equal to that of the market portfolio. So the statement is false

c) The statement is true and almost 90-95% of the unsystematic risk can be diversified away with 20-30 assets and further adding of assets to the portfolio decreases the risk very slowly

c) Idiosyncratic risk is a risk which is specific to the asset or the asset class. This risk is also called as unsystematic risk and can be diversified by holding different kind of assets in the portfolio. Systematic risk on the other hand , is the risk which one has to take and cannot be diversified away.

Total risk of an asset = systematic risk (represented by Beta) + idiosyncratic risk

The relationship with premium is that market does not reward any person for taking unsystematic or idiosyncratic risk. Only the systematic portion of the risk (represented by beta) is rewarded. Beta represents the systematic part of the risk.  So, the relationship is as per Capital Assets pricing model

Risk premium of any asset over risk free rate= Beta of asset * (market return- risk free rate)