8. 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 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? Additional assumptions made in the calculations: (a) Assume the bond portfolio is restructured annually to maintain a duration of 10 years (b) Assume the value of money borrowed is maintained at $12.5 billion every year (c) Assume Orange County makes interest on borrowed fund at the rate which prevailed at the beginning of the given year. Hints