8. vialn 1.25 points magine you are a provider of portfolio insurance. You are e

Question

8. vialn 1.25 points magine you are a provider of portfolio insurance. You are establishing a four-year program. The portfolio you manage is currently worth $170 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 5.8% 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 porfolio 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 illion b-2. What action should the manager take? (Enter your answer in millions rounded to 2 decimal places.) The manager must (Click to select) $ (Click to select) million of (Click to select) and use the proceeds to (Click to select) (Click to select)and use the proceeds to (Click to select)

Explanation / Answer

S= current value of the portfolio = $170 million

X= floor price promised = $170 million

sd= standard deviation of the equity portfolio = 0.25

rf= riskfree t-bill rate = 5.8%

time horizon = 4 years

No dividends is paid

a-1: Applyling the Black Scholes formula-

N(d1)= 0.7625

The put price is calculated to be $15.585

So, total funds = $170+$15.585 = $185.585 million

The funds include the portfolio value and the funds allocated for the insurance.

As, N(d1) = delta of call option

Delta of put option = N(d1)-1 = -0.2375

So, 23.75% of the equity portfolio has to be sold and invested in T-bills.

So, 0.7625*170 = $129.625 is kept in equity

The remaining that is $185.585-$129.625= $55.96 million is invested in treasury bills.

Stock portfolio falls by 3%. So, new portfolio value = $164.9 million

Hence, again by applying Black Scholes: put value = $16.845

N(d1) call = 0.7432

So, delta put = 1-0.7432 = -0.2568

So, equity shares sold = 25.68% of $164.9 million = $42.346 million

These equity shares have to be sold and invested in treasury bills.

Total funds available = $164.9+16.845= $181.745

Equity share = $122.55 million

So funds in treasury bills = $59.19 million

The portfolio value now is $164.9 million

So, ANSWER:

a-1: portfolio in bills = 23.75%

a-2: portfolio in equity = 76.25%

b-1: put delta: -0.2568

amount held in bills : $59.19 million

b-2:The manager must sell $42.346 million of equity stocks and use the proceeds to buy treasury bills.

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