Question

An investor currently has $50M in the Alibaba stock and $50M in one-year zero-coupon bonds. Assume that the one-year interest rate is 8% (annually compounding). Assume that the current quote on the Alibaba stock is 1,250, each futures contract is written on 200 shares of the Alibaba stock and the dividend yield on the stock is approximately 3% per year, i.e., $1,000 invested in the stock yields $30 in dividends at the end of the year.

(a) Suppose you invest $1,250×200 in one-year zero-coupon bonds and at the same time enter into a single futures contract with long position on the Alibaba with one year to maturity. Assume that in one year the stock finishes at 1,100. What is the total value of your position?  How does this compare with buying 200 shares of the stock and holding them for a year?

(b) If this investor decides to switch to a 70/30 stock/bond mix for a period of one year, how would he/she implement this strategy using the Alibaba futures?  How many contracts with one year to maturity would you need?

Answer 1

a.

Future price = S₀ * (1+ r )^t = 1250 * ( 1 +0.08 )¹= $1250 * 1.08 = $1350

where

S₀ is current share price

r = risk free rate

t = time

note here we do not consider dividend because it will receive end of the year

price of bond = S0 * (1+r)^t =$ 1250 * (1.08)¹ = $1350.

Total value of bond = 200*$1350 = $270000

value of future contract = ( ST - F ) no of contract = ($1100 - $1350) 200 = -$250*200 = -$ 50000

where ST is share value at the end of year

F is future price.

Total value of position = value of bond + total value of equity = $270000 - $50000 = $220000

if we we 200 share then the value of share = $1100 * $200 = 220000 so equal to above position

note Long on share = Long on future + long on risk free bond

in above case its hold true.

  

b.

current ratio of Bond and Equity is 50 :50

to change ratio by 70:30

so we need to buy equity of 20M so new equity value = $20M +$ 50M

and we need to sell bond of 20M so bond value = $50M -$ 20 M = $30M

NO of bond need to sell = value of bond need to sell / price of bond = -$20000000 / 1350 = 14814.81 = 14815 bond

No of future contract need to buy = value of equity need to buy / price of future contract = $20000000 / $1350 = 14814.81 = 14815 future contract