Question

Imagine 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 for that all dividends are reinvested) 0-1. 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 bils % 0-2. 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 os a positive value. Do not round intermediate calculations. Round your answers to 2 decimal places.) Put delta Amount held in bills 1 million

Answer 1

In this case, minimum return promised is 0%, so the portfolio at the year end should not fall below $170 million.

Standard deviation of equity portfolio is 25% i.e. amount invested in equity may fall by 25%, so we have to find out the combination of debt and equity so that the portfolio should not fall below $170 million after 1 year by following calculation.

:. 170 = 170 + [(170* P%)*5.8%] - [(170*(1-P%)) * 25%]

Where, P = Weight of portfolio invested in Debt

:.170 = 170 + 0.0986P - 42.5 + 0.425P

So, P = 81.1688%

1-P = 18.8312%

PERCENTAGE OF PORTFOLIO INVESTED IN BILLS:

= 170 * 81.1688%

= $137.99 million

So, $137.99 million should be invested in bills

PERCENTAGE OF PORTFOLIO INVESTED IN EQUITY:

= 170 * 18.8312%

= $32.01 million

So, $32.01 million should be invested in equity

PUT DELTA IF THE STOCK PORTFOLIO FALLS BY 3%

Equity falls by 3%. So the amount of equity in portfolio will be

= 32.01 * 97%

= $31.05 million

Amount in bills will be the same i.e. $137.99 million as market volatility does not affect risk free investment.

So the total amount of Portfolio will be = 31.05 + 137.99

= $ 169.04 million

% of Decrease in portfolio

= (170 - 169.04) / 170

= 0.56%

Put Delta =

$\frac{PercentageChange in Portfolio}{Percentage Change in Market}$

$\frac{0.56}{3}$

= 0.1867

Put Delta is 0.1867

In this case, Manager should take action to maintain the portfolio of $170 million, so he should transfer amount as calculated below to bills from equity

:. 170 = 169.04 + [(169.04* P%)*5.8%] - [(169.04*(1-P%)) * 25%]

P = 83.02%

1-P = 16.98%

So, the final combination of portfolio should be $141.13 million (170*83.02%) in bills and $28.87 million in equity. Accordingly the fund manager should take action to transfer funds from equity to bills.