Question

Imagine you are a provider of portfolio insurance. You are establishing a four-year program. The portfolio you manage is currently worth $160 million, and you promise to provide a minimum return of 0%. The equity portfolio has a standard deviation of 25% per year, and T-bills pay 6.5% per year. Assume for simplicity that the portfolio pays no dividends (or that all dividends are reinvested).

a-1. What percentage of the portfolio should be placed in bills? (Input the value as a positive value. Round your answer to 2 decimal places.)

Portfolio in bills             %

a-2. What percentage of the portfolio should be placed in equity? (Input the value as a positive value. Round your answer to 2 decimal places.)

Portfolio in equity             %

b-1. Calculate the put delta and the amount held in bills if the stock portfolio falls by 3% on the first day of trading, before the hedge is in place? (Input the value as a positive value. Do not round intermediate calculations. Round your answers to 2 decimal places.)

Put delta		%
Amount held in bills	$	million

b-2. What action should the manager take? (Enter your answer in millions rounded to 2 decimal places.)

The manager must (Click to select)sellbuy $  million of (Click to select)billsequity and use the proceeds to (Click to select)sellbuy (Click to select)billsequity.

Answer 1

160 =160+[(160*p%)*6.5%]- [(160*(1 -P%)*25%]

160 = 160+0.1040P-40 +0.40P

40 =0.504p

p= 79.36%

1-p=20.64%

a-1. What percentage of the portfolio should be placed in bills? (Input the value as a positive value. Round your answer to 2 decimal places.)

Portfolio in bills =79.36% %

Amount invested in bills =160*79.36%=126.97

a-2. What percentage of the portfolio should be placed in equity? (Input the value as a positive value. Round your answer to 2 decimal places.)

Portfolio in equity =20.64 %

Amount invested in Equity = 160*20.64% =$33.03 million

b-1. Calculate the put delta and the amount held in bills if the stock portfolio falls by 3% on the first day of trading, before the hedge is in place? (Input the value as a positive value. Do not round intermediate calculations. Round your answers to 2 decimal places.)

If Stock portfolio falls by 3% amount of equity will be =33.03*97%=$32.039 Million

Now total portfilio is = $32.039+$126.97=$159.009

Percentage of decrease in portfolio =(160-159.009)/160 =0.62%

Put Delta= %change in portfolio/ % change in Market

=0.62/3=0.2066

Put delta		0.2066
Amount held in bills	$	million

b-2. What action should the manager take? (Enter your answer in millions rounded to 2 decimal places.)

160 =159.009+[(159.009*p%)*6.5%]- [(159.009*(1 -P%)*25%]

160 = 159.009+0.1033P-39.75 +0.3975P

160-159.009 +39.75 =0.5008p

40.74= 0.5008p

p=81.35%

1-p=18.65%

Bills should be =160*81.35%= 130.16

Equity =160*18.65%=29.84

Final combination of Bills and equity will be $130.16 and $29.84

Manager will Sell equity and buy bills accordingly