Class 9: Efficient Portfolios

Question 1

Portfolio Variance

Answer 1

Var(r_portfolio)= W²_AVar(r_A)+W²_BVar(r_B)+2W_<u>A</u> W_<u>B</u> Cov(r_<u>A</u>, r_<u>B</u>) _→_Diversification

Question 2

The expected return of a portfolio is…

Answer 2

E[r_p] = W_Ar_A + W_Br_B

In a portfolio with short sales the only difference here is that one of these weights is going to be negative

Question 3

The standard deviation of the portfolio is:

Answer 3

SD_p = √W_A² σ_A² + W_B² σ_B² + 2W_AW_B COV_A,_B

The standard deviation is basically the square root of the variance. With short sales, the portfolio will most likely have a higher volatility because borrowing increases risk (and expected return).

Question 4

According to this graph, what happens when you long Intel and your weight is 1.5?

Answer 4

As you short Coca-Cola and you long Intel, you are basically moving up the curve. The expected return is higher, but things become riskier and riskier.

Question 5

What’s the portfolio expected return of 3 stocks?

Answer 5

E[r_p] = W_Ar_A + W_Br_B + W_cr_c

It’s the same logic as two stocks, you just need to add the third stock “C”. Remember that the weights of these 3 stocks have to add up to 1.

Question 6

How do you calculate the covariance of three stocks?

Answer 6

YOU CAN’T! Remember that covariance is only between 2 things. There is no such thing as covariance of 3 things. If you want to calculate the covariance in a 3 stock scenario, you would need to calculate 3 separate pairs of covariances.

Question 7

What’s the efficient frontier?

Answer 7

It’s the limit on how far you can go, the efficient frontier = the best portfolios with MAXIMUM returns and MINIMUM standard deviation. If the covariances between 3 stocks is lower, then the efficient frontier would move to the left.

Question 8

What happens to diversification as you add more stocks?

Answer 8

Any addition of a stock gives you one more covariance to play with, and it gives you more diversification. The more stocks you buy the more you can move left, this all depends on the covariances. Any marginal covariance gives you diversification space.

And it’s a surface because there are MANY portfolios, at the frontier are the best ones, the most efficient ones.

Question 9

How do you build a Portfolio Variance-covariance matrix?

Answer 9

It’s an NxN matrix, the diagonal terms are W₁²σ₁²**for example, and the off diagonal terms areW₁W₂COV_1,2** for example.