FINANCIAL MARKETS AND FINANCIAL INSTRUMENTS

Financial Markets and Financial Instruments

Financial Markets and Financial Instruments

Question 2

Variance of an Equally Weighted Portfolio

Kp = ½ × kp1 + ½ × kp1+½ × kp1 ='1/2 × 15% + 1/2× 20% = 7.5% % 10% ' 17.5%

Obviously, if you invest 75% in Stock 1, then the weights will be (3/4) and (1/4) respectively.

Measures of Co-Movement

Absolute measure: Co-variance of x and y / cov(x,y)

Thus,

If cov(x,y) is < 0, then x and y move in opposite direction

If cov(x,y) is > 0, then x and y move in same direction

If cov(x,y) is = 0, then x and y have no systematic co-movement

B

Variance of portfolio

boom:rp = .25(14) + .25(18) + .50(26) = 21%

bust:rp = .25(8) + .25(2) + .50(-2) = 1.5%

rp = .65(21) + .35(15) = 14.175%



So

s 2p= .65(21 - 14.175)2 + .35(15 - 14.175)2 = 30.515

Total Stand Alone Risk = si2= Market Risk + Firm Specific Risk

Market Risk - Risk of Security that cannot be diversified away - Measures by beta also called Systematic Risk.

Firm Specific Risk - Portion of Security's risk that can be diversified away, also called unsystematic risk. The variance of a portfolio is equal to the weighted average covariance of each stock with the portfolio:

This reduces to:

A point that we noted from the calculations of expected portfolio returns and variances above was that, in all of our calculations, the variance of the portfolio return was lower than that on any individual component's asset return (Miller, 1999). To illustrate this point in a general setting, consider the following scenario. An investor holds a portfolio consisting of N stocks; with each stock having the same portfolio weight (i.e. each stock has portfolio weight N-1). Denote the return variances for the individual assets by s2 i where i = 1 to N, and the covariance between returns on assets i and j by sij. Equation 1

Examining the second term of equation 2.10, the existence of N component assets implies that the summation for all i not equal to j involves N (N - 1) terms. Obviously the summation in the first term of 2.10 involves N terms. Hence, defining the average variance of the N assets as s-2 and average covariance across all assets as EQ, 2:

Equation 2

Equation (2) obviously simplifies to the following

Equation 3

How does the portfolio variance change as the number of assets combined in the portfolio ...