diversification - Portfolio theory

Question 1

how to calculate covaraince?

Answer 1

Cov_p = P_E,F x σ_Eσ_F

Question 2

what is the weighted average standard deviation of 2 assets

Answer 2

w₁σ₁ + w₂σ₂

if this is greater than σp, there is a diversification benefit

Question 3

what does it mean when an asset’s weight is negative?

Answer 3

The weight in Asset 1 is negative, and, therefore, the weight in Asset 2 is over 100%. This is because we are “short-selling” Asset 1 and putting all our money, plus the money we get from the short-sale, into Asset 2.

Short-selling involves selling assets you do not own. We borrow Asset 1 and sell it in the market. At a later date, we will have to buy back Asset 1 and return it to the person we borrowed it from

Question 4

short selling often occurs when

Answer 4

we expect an asset to drop in price, in which case we would sell while the price is high and buy it back once it has dropped. However, there is no guarantee the price will fall as we expect. If the price rises instead of falls, we would have to buy the stock back at a loss.

Question 5

how to determine whether diversification has helped reduce risk?

Answer 5

We know conceptually that the answer must be “no”, as the assets have a perfect positive correlation. However to see this, we can calculate the weighted average risk of the two assets, using their weights in the minimum variance portfolio:

(-1.667 x 8%) + (2.667 x 5%) = 0.00%

Question 6

Briefly outline the benefits of diversification. In providing an answer, make sure you discuss how diversification benefits are maximised.

Answer 6

By putting two assets that do not move perfectly with one another together in a portfolio, investors can achieve diversification benefits. Specifically, they can obtain a reduction in risk without sacrificing any expected return. This occurs as movements in the price of one asset cancels out movements in that of the other. The extent of any diversification benefits will be a function of how the assets move relative to one another. This is measured by how highly correlated the assets are with one another. In order to achieve maximum diversification benefits, the assets should be perfectly negatively correlated with one another. However, diversification benefits will still be available for assets with less than perfect positive correlation, though these benefits will decrease as the coefficient of correlation between the assets increases.