1.

a. Take a bond portfolio whose modified duration is -5; the portfolio's value is $2,000,000. How much will the portfolio value change if the yield rises by 1 basis point (0.01% or 0.0001)? (Formula 1)

b. If you want to hedge this portfolio against an increase in yield (decline in value) using a different bond whose modified duration is -10, will you buy or sell this hedge bond, and how much in value (i.e. not principal amount) will you buy or sell? (Formula 2)

2.

a. Take a stock that you intend to buy with a value of $5,000,000 and whose beta β is 1.05. How much will the the portfolio value change if the S&P500 ("The Market") rises by 5%? (Formula 1) 

b. If you hedge this portfolio against an increase in value using a different stock whose β is 1.0, will you buy or sell this hedge stock, and how much will you buy or sell? (Formula 2)