An investor has decided to model PPB ple shares using the lognormal model. Using historical data, she has estimated the drift and volatility parameters to be 6% and 25% respectively. PPB's current share price is $2. (i) (ii) Calculate the mean and variance of PPB's share price in one year's time. [3] Calculate the probability that: (a) PPB's shares fall in value over the next year. (b) PPB's shares yield a return of greater than 30% over the next year. Assume that no dividends are to be paid over the next year. [4] [Total 7] Imagine you find a horse race involving just three horses and you notice that the odds are as follows: Nag Portachio GG Badeye Horsey Mullet evens 3/1 7/1 Devise a betting strategy to make an arbitrage profit. Note that, in gambling, 3/1 means that if you put a 1 bet on and GG Badeye wins then you receive 3 + 1 = 4. "Evens" means 1/1.