Question

3. An investor is concerned with the market return for the coming year, where the market return is defined as the percentage gain ( or loss, if negative) over the year. The investor believes there are five possible scenarios for the national economy in the coming year- rapid expansions, moderate expansions, no growth, moderate contractions and serious contraction. Furthermore, she has used all of the information available to her to estimate that the market returns for these scenarios are, respectively 23%, 18%,15%,9% and 3% .Also she has assessed the probabilities of these outcomes are 0.12, 0.40,0.25, 0.15 and 0.08. Use this information to describe the probability distribution of the market return. Calculate, average return, standard deviation and variance of the probability distribution of the market return for the coming year and comment.

Answer 1

Average of portfolio E(r) =   p(s)*r(s),

where p(s) is the probability of each scenario,

and r(s) is the expected return of each scenario.

Variance of portfolio ²  = p(s)*[r(s) - E(r)]²

where [r(s) - E(r)]² is the squared deviation from the average return.

Standard deviation =  variance

The average return of the probability distribution is 15.30% with a standard deviation of 5.30%.

The market has an expected return of 15.30%.