Question

Based on Modern Portfolio Theory, explain what the variance and covariance terms are capturing. Which is a more relevant measure in a well-diversified portfolio? Briefly explain. If a portfolio has 5 individual stocks in it, how many total variance and covariance terms are there?

Answer 1

Covariance is a statistical measure which tells us the directonal relationship between the returns on two assets. Covariance can be both positive and negative. Positive covariance means the aseets move in the same direction , while negative covariance means that the assets move in the opposite direction. Where as variance measures the deviation of observed value from its expected value. This value is always positive and also tells us about the riskiness of the stock. Higher the variance higher is the deviation and higher will be the risk of a portfolio.

Covariance is more relevant measure for well diversified portfolio, because it is covariance which tells us wether the portfolio is well diversified or not. Lower the covariance between assets, more diversified the portfolio will be.

If a portfolio has 5 individual stocks, it will have 1 total variance and 10 covariance.

5 portfolio total variance= {(w1^2)(s1^2) + (w2^2)(s2^2) + (w3^2)(s3^2) + (w4^2)(s4^2) + (w5^2)(s5^2)} + {2(w1)(w2)Cov1,2 + 2(w1)(w3)Cov1,3 + 2(w1)(w4)Cov1,4 + 2(w1)(w5)Cov1,5 + 2(w2)(w3)Cov2,3 + 2(w2)(w4)Cov2,4 + 2(w2)(w5)Cov2,5 + 2(w3)(w4)Co3,4 + 2(w3)(w5)Cov3,5 + 2(w4)(w5)Cov4,5}