10. (Orange County blues) Orange County managed an investment pool into which several municipalities made short-term investments A total of $7.5 billion was invested in this pool, and this money was used to purchase securities. Using these securities as collateral, the pool borrowed $12 5 billion from Wall Street brokerages, and these funds were used to purchase additional securities The $20 billion total was invested primarily in long-term fixed-income securities to obtain a higher yield than the short-term alternatives. Furthermore, as interest rates slowly declined, as they did in 1992-1994, an even greater return was obtained Things fell apart in 1994, when interest rates rose sharply Hypothetically, assume that initially the duration of the invested portfolio was 10 years, the short-term rate was 6%, the average coupon interest on the portfolio was 8.5% of face value, the cost of Wall Street money was 7%, and short-term interest rates were falling at % per year

(a) What was the rate of return that pool investors obtained during this early period? Does it compare favorably with the 6% that these investors would have obtained by investing normally in short-term securities?

(b) When interest rates had fallen two percentage points and began increasing at 2% per year, what rate of return was obtained by the pool?