 # Roys safety first criteria

An investor wants to buy a condominium in florida. The vlaue of her portfolio is currently \$1,000,000 and she needs \$100,000 in one year for the down payment. She doesn’t mind decreasing her capital as long she has \$950,000 remaining in her portfolio after the down payment is made. she is considering two new portfolios for her holdings. Expected Annual Return Standard deviation of returns P1 17% 15% P2 12% 10% According to Roy’s safety first criterin, the portfolio she would prefer and the probability that this safety-first optimal portfolio will produce a return of less than 2%(assuming returns are normallu distributed) are : Optimal Port Probability < 2% A> P1 32% B> P1 16% C> P2 32% D> P2 16%

isnt the formula (Rp - target rtn) /(sigma of portfolio) ???

B…P1 is higher safety ratio… (.17-.05)/(.15)= .80 vs. (.12-.05)/.10 = .70 Probability P1 returns less than 2% is (.17-.02)/(.15) = 1…translates to -1 std from the mean of 17%. Look at the Z table and solve for -1 std from the mean and you get 16%.

B SF1 = (.17-.05)/.15 = .80 SF2 = (.12-.05)/.10 = .70 Portfolio 1 is more desirable due to higher SF Ratio. (17 - 2)/15 = 1 Std Dev from the expected return With a normally distributed sample, 68% of all data is within +/- 1 Std Dev from the mean. That leaves 32% of data that exceeds 1 SD, but here you are only interested in the percentage that lies below the 2% mark, so 32/2 = 16% probability. -Stillwagon