Quantitative Problems Chapter 41. You own a $1,000-par zero-coupon bond that has 5 years of remaining maturity. You plan on selling the bond in one year, and believe that the required yield next year will have the following probability distribution:(a) What is your expected price when you sell the bond?(b) What is the standard deviation?Solution:2. Consider a $1,000-par junk bond paying a 12% annual coupon. The issuing company has 20% chance of defaulting this year; in which case, the bond would not pay anything. If the company survives the first year, paying the annual coupon payment, it then has a 25% chance of defaulting the in second year. If the company defaults in the second year, neither the final coupon payment not par value of the bond will be paid. What price must investors pay for this bond to expect a 10% yield to maturity? At that price, what is the expected holding period return? Standard deviation of returns? Assume that periodic cash flows are reinvested at 10%.Solution: The expected cash flow at t1  0.20 (0)  0.80 (120)  963. Last month, corporations supplied $250 billion in bonds to investors at an average market rate of 11.8%. This month, an additional $25 billion in bonds became available, and market rates increased to 12.2%. Assuming a Loanable Funds Framework for interest rates, and that the demand curve remained constant, derive a linear equation for the demand for bonds, using prices instead of interest rates.Solution: First, translated the interest rates into prices.4. An economist has estimated that, near the point of equilibrium, the demand curve and supply curve for bonds can be estimated using the following equations:(a) What is the expected equilibrium price and quantity of bonds in this market?(b) Given your answer to part a., which is the expected interest rate in this market?Solution:(a) Solve the equations simultaneously:(b)5. As in question 6, the demand curve and supply curve for bonds are estimated using the following equations:Solution:6. Following question 5, the demand curve and supply curve for bonds are estimated using the following equations:Solution: Prior to the change in inflation, the equilibrium was Q  350.00 and P  850.00 The new equilibrium price can be found as follows:Quantitative Problems Chapter 41. You own a $1,000-par zero-coupon bond that has 5 years of remaining maturity. You plan onselling the bond in one year, and believe that the required yield next year will have the following probability distribution:Probability Required Yield0.1 6.60%0.2 6.75%0.4 7.00%0.2 7.20%0.1 7.45%(a) What is your expected price when you sell the bond?(b) What is the standard deviation?Solution:Probability Required Yield Price Prob  PriceProb * (Price –Exp. Price)20.1 6.60% $774.41 $77.44 12.847762410.2 6.75% $770.07 $154.01 9.7756681310.4 7.00% $762.90 $305.16 0.0130175120.2 7.20% $757.22 $151.44 6.8626095410.1 7.45% $750.02 $75.02 16.5903224$763.07 46.08937999The expected price is $763.07.The variance is $46.09, or a standard deviation of $6.79.2. Consider a $1,000-par junk bond paying a 12% annual coupon. The issuing company has 20% chance of defaulting this year; in which case, the bond would not pay anything. If the company survives the first year, paying the annual coupon payment, it then has a 25% chanceof defaulting the in second year. If the company defaults in the second year, neither the final coupon payment not par value of the bond will be paid. What price must investors pay for this bond to expect a 10% yield to maturity? At that price, what is the expected holding period return? Standard deviation of returns? Assume that periodic cash flows are reinvested at 10%.Solution: The expected cash flow at t1  0.20 (0)  0.80 (120)  96The expected cash flow at t2  0.25 (0)  0.75 (1,120)  840The price today should be: 0296 840781.491.10 1.10P   At the end of two years, the following cash flows and probabilities exist:Probability Final Cash Flow Holding Period Return Prob  HPRProb * (HPR – Exp. HPR)20.2 $0.00 100.00% 20.00% 19.80%0.2 $132.00 83.11% 16.62% 13.65%0.6 $1,252.00 60.21% 36.12% 22.11%0.50% 55.56%The expected holding period return is almost zero (0.5%). The standard deviation is roughly 74.5% [the square root of 55.56%].3. Last month, corporations supplied $250 billion in bonds to investors at an average market rate of 11.8%. This month, an additional $25 billion in bonds became available, and market rates increased to 12.2%. Assuming a Loanable Funds Framework for interest rates, and that the demand curve remained constant, derive a linear equation for the demand for bonds, using prices instead of interest rates.Solution: First, translated the interest rates into prices.100011.8% , or 894.454Pi PP  100012.2% , or 891.266Pi PP  We know two points on the demand curve:P  891.266, Q  275P  894.454, Q  250So, the slope  891.266 894.4540.12755275 250PQ   Using the point-slope form of the line, Price  0.12755  Quantity  Constant. We can substitute in either point to determine the constant. Let’s use the first point:891.266  0.12755  275  constant, or constant  856.189Finally, we have:Bd: Price  0.12755  Quantity  856.1894. An economist has estimated that, near the point of equilibrium, the demand curve and supplycurve for bonds can be estimated using the following equations:Bd: Price  2 9405QuantityBs: Price  Quantity  500(a) What is the expected equilibrium price and quantity of bonds in this market?(b) Given your answer to part a., which is the expected interest rate in this market?Solution:(a) Solve the equations simultaneously:2940550070 440, or 314.28575P Q[P Q ]Q Q     This implies that P  814.2857.(b)1000 814.285722.8%814.2857i 5. As in question 6, the demand curve and supply curve for bonds are estimated using the following equations:Bd: Price  2 9405QuantityBs: Price  Quantity  500Following a dramatic increase in the value of the stock market, many retirees started moving money out of the stock market and into bonds. This resulted in a parallel shift in the demand for bonds, such that the price of bonds at all quantities increased $50. Assuming no change in the supply equation for bonds, what is the new equilibrium price and quantity? What is thenew market interest rate?Solution:The new demand