In January 2006, three bond investors, Mary Isaacs, Katie Ingersoll, and Ron Ip,
ID: 2714116 • Letter: I
Question
In January 2006, three bond investors, Mary Isaacs, Katie Ingersoll, and Ron Ip, each bought $1 million worth of bonds. All bonds in this question have an annual coupon period. All three bond investors bought only newly issued bonds, and the bonds were all sold for face value and hence had coupon rates equal to their yields when issued. They neither added money to their bond investing accounts nor took any out: they reinvested any coupon or principal repayments according to the strategies below, until January 2009, when they compared their wealth. Every January, Mary invested everything in bonds with a 1-year maturity. Katie always bought bonds with maturity January 2009. In January 2006, Ron bought bonds with a 5-year maturity. He did so again in January 2007. In January 2008, he bought bonds with a 1-year maturity. Mary and Katie never sold any bonds before maturity. Ron only sold bonds that hadn't matured yet in January 2009. The table below shows yield curves each January. How much money did Mary, Katie, and Ron each have in January 2009? Who took on the least interest-rate and reinvestment risk? Who took on the most? Explain your reasoning.Explanation / Answer
a)
Case 1 - Mary
In Jan 2006 - She bought 1 year bonds with coupon rate of 5.4%. After 1 year she gets 1000000 * 1.054 = $1054000. She invests this in 1 year bonds with coupon rate of 6% giving a value of 1054000 * 1.06 = $1117240. She invests the proceeds in1 year bonds with coupon of 3.9% giving her 1117240 * 1.039 = $1160812.36 in Jan 2009.
Case 2 - Katie
In Jan 2006 - She bought 3 year bonds with coupon rate of 5.3%. After 1 year she gets a coupon of 1000000 * .053 = $53000. She invests this in 2 year bonds with coupon rate of 5.8% giving a combined coupon of 1000000 * 0.053 + 53000 * 0.058 = $56074 in Jan 2008. She invests the proceeds in 1 year bonds with coupon of 3.9% giving her a funds worth 1000000 * 1.053 + 53000 * 1.058 + 56074 * 1.039 = $1167334.89 in Jan 2009.
Case 3 - Ron
In Jan 2006 - She bought 5 year bonds with coupon rate of 5.3%. After 1 year she gets a coupon of 1000000 * .053 = $53000. She invests this in 5 year bonds with coupon rate of 5.7% giving a combined coupon of 1000000 * 0.053 + 53000 * 0.057 = $56021 in Jan 2008. She invests the proceeds in 1 year bonds with coupon of 3.9% giving her a combined coupon worth 1000000 * .053 + 53000 * .057 + 56021 * .039 = 53000 + 3021 + 2184.82 = $58205.82.
One year bond bought in 2008 matures giving funds worth $56021.
Value of bonds bought in 2006 =PV(1.7%,2,53000,1000000) = $1070204.75
Value of bonds bought in 2007 =PV(2%,3,3021,53000) = $58655.30
Total funds with Ron = 58205.82 + 56021 + 1070204.75 + 58655.30 = $1243086.86
b) Least Interest Rate Risk is taken by Mary because she bought bonds with the shortest maturity that is 1 year. However, since Mary and Katie did not sell bonds prior to maturity, they are effectively took no interest rate risk. Interest rate risk is change in the value of the bond due to changes in the interest rate in the market. Since, they the bonds mature, they did not take any interest rate risk. Most interest rate risk is taken by Ron as he bought bonds with longest maturity and sold bonds prior to maturity which led to a change in the value of the bonds.
Most Reinvestment Risk is taken by Mary since she is buying bonds with the shortest maturity and thus, has to reinvest both the interest and principal every year unlike Katie and Ron who only have to reinvest the interest and not the principal. The least reinvestment risk was taken by Ron till Jan 2009 as he bought bonds with longest maturity (5 years in 2006 and 2007) as compared to 3 years and 2 years by Katie in 2006 and 2007. Although, Ron sold off all the bonds in 2009 Jan as compared to the natural maturity of bonds bought by Katie leaving Ron with more funds to reinvest. Still , uptill 2009 Jan, Ron took the least reinvestment risk.
Jan-06 Jan-07 Jan-08 Jan-09 Mary 1000000 1054000 1117240 1160812.36 Katie 1000000 53000 56074 1167334.89 Ron 1000000 53000 56021 1243086.86Related Questions
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