FINAL EXAM REVIEW GUIDE Chapters 10 and 11 Bonds Calculating bond prices yields coupons return Bond price present value of cash flows discounted at the market required rate of C C Par PV C 1 r 1 1 r 2 1 r t Where C Coupon per period PMT Par Face or maturity value FV r Interest rate r or YTM t Compounding periods to maturity o Bond prices vary inversely with interest rates If the market interest rate is below the interest rate on the bond the price and value of the bond will go up The coupon rate is based on the par value of the bond and determines periodic interest payments It is usually fixed throughout the term The yield to maturity is the annual yield that equates the future coupon and principal payments with the bond price The YTM is the investor s expected rate of return if the bond is held to maturity In other words the discount rate that makes the present value of a bond s payments equal to its price o Determinants of bond yields include Term to maturity Default risk Liquidity Tax status Special option features such as convertibility and call and put features o The yield can be found by r FV PV 1 t 1 Premium discount and par bonds A par bond s yield to maturity is equal to the coupon rate and sells at par value A discount bond s yield to maturity is greater than its coupon rate and sells below A premium bond s yield to maturity is less than its coupon rate and sells above par value par value Price path of bonds over time Bond Value rd 7 rd 10 1 372 1 211 1 000 837 775 Years remaining to Maturity rd 13 15 10 5 0 M 30 25 20 As the bond gets closer to maturing it will be less sensitive to a change in interest rates If the bond is far away from its maturity date the price will fluctuate greatly with a small change in interest rates because that interest rate has longer to affect the coupon payments of the bond Bond volatility sensitivity to changes in interest rates The value of discount bonds especially zero coupon bonds is more sensitive to changes in interest rates than the value of otherwise comparable coupon bonds because a low coupon bond s PV of face value at maturity is a major proportion of the price small or no monthly payments to hedge interest rate risk Long term bonds are more sensitive to changes in interest rates because the changed rate will be compounded more frequently before the bond matures Duration A measure of the effective maturity of a bond defined as the weighted average of the times until each payment with weights proportional to the present value of the payment Duration measures how price sensitive a security is to a change in interest rates The longer a bond s duration the greater its sensitivity to interest rate changes Duration sum of discounted time weighted cash flows divided by price and is a measure of effective maturity that incorporates the timing and size of a security s cash flows The duration of a zero coupon bond bond s term to maturity The duration of any coupon bond is always less than the bond s term to maturity With time to maturity and yield to maturity held constant a bond s duration and interest rate sensitivity are higher when the coupon rate is lower The duration of a perpetuity is 1 y y Immunization A strategy to shield net worth from interest rate movements The theory behind immunization is that you can hedge interest rate risk by taking simultaneous positions in two different bonds For example you buy a one year bond with a 10 interest rate and a three year bond with a 10 interest rate and you want to cash out after two years You will hold the one year bond for the first year and then purchase another bond at the current interest rates for the second year With the three year bond you hold it for two years and then sell it with the price dependent on the current interest rates If interest rates rise it will positively affect the return on your reinvested 1 year bond and negatively affect the return on the 3 year bond When weighted properly the two differences in return can cancel out and hedge the risk EX Bond manager has 830 000 to invest but must fulfill an obligation of 1 million in 2 years o Suppose there are only two zero coupon bonds available in which to invest 1 maturity 1yr yield 10 2 maturity 3yr yield 10 o Immunization strategy says that you should set the duration 2 Dp W1D1 W2D2 They are both zero coupon bonds so D1 1 and D2 3 which means W1 5 and W2 5 o Calculated proof if interest rates rise to 12 in thousands 415 1 1 456 5 1 12 511 28 415 1 1 3 552 4 1 12 discounted back to yr 2 493 21 511 28 493 21 1004 49 This is the same profit as if the interest rate had remained at 10 and not risen to 12 Problems with Immunization o Default and call risk immunization strategies assume all bond cash flows will be paid in full and on time which is not realistic in the real world o Non horizontal yield curves and nonparallel shifts o Real world combinations Durations of assets and liabilities may differ causing a change in interest rates to affect each side of the balance sheet to a different degree Chapters 15 16 Options Definitions call put Call Option A contract that gives the owner the right but not the obligation to buy a stock at a fixed price exercise or strike price on or before a given date expiration date Put Option A contract that gives the owner the right but not the obligation to sell a stock at a fixed price exercise or strike price on or before a given date expiration date In the money at the money out of the money A call option is A put option is o In the money when the stock price is higher than the strike price because you could exercise your option at the strike price and immediately sell it at the current stock price for a profit o At the money when the stock price equals the strike price o Out of the money when the stock price is below the strike price because you could buy the stock in the market for less money than you could if you exercised your option o In the money when the stock price is less than the strike price because you could buy stocks at the market price and immediately sell them for a profit at the strike price o At the money when the stock price equals the strike price o Out of the money when the stock price is greater than the strike price because you could sell the stocks …