Suppose there are N risky assets and one risk free asset. Every investor can bor

Question

Suppose there are N risky assets and one risk free asset. Every investor can borrow or lend freely at the risk-free asset. Suppose further that every investor has homogeneous expectation on stock returns. In this case, explain briefly why the tangency portfolio should be the market portfolio. Market portfolio is defined as the weighted average of individual stock returns. The weight of each stock in this portfolio is defined as the market capitalization of the firm over the total market capitalization of all stocks.

Explanation / Answer

Meaning :-

Let us understand the meaning of Tangency portfolio -

Market portfolio as given is defined as the weighted average of individual stock returns. The weight of each stock in this portfolio is defined as the market capitalization of the firm over the total market capitalization of all stocks.

Analysis :-

In this case if the market portfolio is inefficient then investors can take advantage of miss-pricings as they have homogeneous expectations on stock returns and this would result in a tangency portfolio with efficient returns.

The investors having homogeneous expectations are those who if have a choice in several investment plans with same risk factor but different returns, they will choose the plan which will give highest return or several investment plans with same return factor but different risk, then they will choose the plan which has lower risk.This will have an impact on the arbitrage.  

Advantages of market portfolio :-

Here, though there is one risk free asset with N risky assets still the expected returns cannot be stated individually and market portfolio will help to determine the risk associated with total portfolio.

So, tangency portfolio should be the market portfolio

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