Question

Problem 1 You are holding an all-equity (unlevered) portfolio Q with rf-5%, Rm-10%, Rq-109. ơ,-2096. a) What will be the debt-equity of a levered portfolio that will have 30% volatility? b) How much you will borrow if your all-equity portfolio is worth $50,000? c) How much will be invested in the portfolio Q you now hold to create the levered portfolio in part (a)?

Answer 1

Part a)

R_q = R_m = 10%

Hence, beta of portfolio Q = B_Q = beta of market portfolio = B_M = 1

Let's assume the proportion of portfolio Q in the levered portfolio is w. The volatility of the levered portfolio = w x σ_Q = 0.20w

We want the volatility of the levered portfolio to be 30% = 0.30

hence, 0.20w = 0.30

Hence, w = 0.30 / 0.20 = 1.50 = 150%

If B is the amount borrowed and Q is the value of unlevered portfolio, then (B + Q) / Q = 150%

Or, B / Q = 150% - 100% = 50%

B/Q = debt to equity ratio of the levered portfolio = 50%

Part (b)

B / Q = 50%, Q = $ 50,000

Hence, amount borrowed, B = 50% x Q = 50% x 50,000 = $ 25,000

Part (c) Amount invested in portfolio Q as part of levered portfolio = B + Q = 25,000 + 50,000 = $ 75,000