An example of the benefits of diversification

Setup There are two assets 1.Ebay 2.IBM There are two equally likely states of the world 1.State 1 (occurs with probability 1/2) 2.State 2 (occurs with probability 1/2)

Returns EbayIBM State 13%1% State 21%3% Depending on whether state 1 or state 2 occurs, the returns on the two assets will be as described in the table

Can you compute expected returns, volatilities?

What about the correlation?

Question 1 This two assets look exactly the same, at least if we only look at their expected returns and volatilities. Why should we invest in both of them? Couldn’t we just pick one of the two?

Question 2 This assets are perfectly negatively correlated. Wait a minute: does this mean that investing in both of them is going to drive down the expected return of my portfolio?

Let’s figure this out… Say that you split your portfolio in equal shares, i.e. w IBM =w EBAY =0.5. What is the expected return of your portfolio? What is the variance of the portfolio?

This means that… By combining the two assets, we managed to get a portfolio with the same expected return as either of the two assets, but with no risk, i.e. with zero variance

Answer to question 1 Investing in both assets is always a superior strategy to putting all your money in only one asset, because you can obtain the same expected return with a much lower amount of risk!

Answer to question 2 Investing in two assets that are negatively correlated does not necessarily mean that your returns will be lower in expectation. This example shows that you can obtain a portfolio with exactly the same expected return.