Chapter 7
What is the formula to find a present value of the principal
Future Value of Principal PV= (1+r)ⁿ r=discount rate n= # of compounding periods
What happens to an investor's return when inflation is higher than expected?
If the inflation rate is higher than expected, the investor's real rate of return will be lower than expected. An unexpected change in the inflation rate also affects the real rate of return. An investor lending money will demand an interest rate based on her expectations for inflation.
What happens to the real rate of return during a recession?
Real interest rates tend to be cyclical, rising during periods of economic growth and falling during recessions. The supply of and demand for funds are key determinants of the real rate. Demand for funds increases when business conditions improve and the economy looks strong.
What is the formula to find a present value of a bond
The formula for PV of principal and the formula for the PV of an annuity added together
What is the formula to find a present value of annuity (income stream)
⌈ 1- __1__ ⌉ (1+r)ⁿ __________ APV=C x r ⌊ ⌋ c=payment (the value of one coupon payment) r=discount rate n= # of compounding periods
What is the formula for finding a treasury bill yield?
100-price x 365 x 100 ------------ ----- price term
What is the formula to find a current yield of a bond?
Current Yield = Annual Cash Flow (coupon rate) ------------------------------------------ x 100 Current Market Price
If investors expect inflation to be 3% next year and the nominal interest rate on a GIC is 5%, what is the real rate of return on this investment?
For this GIC, the real return is 2%, calculated as 5% - 3%. The real interest rate accounts for the negative effects of inflation.
What expectations are implicit in a downward sloping yield curve? a)Investors expect rates to fall in the future. b)Investors expect rates to rise in the future. c)Investors expect rates to rise then fall. d)Investors expect rates to remain fairly stable.
a)A downward sloping yield curve, where short-term rates are higher than long-term rates, indicates that investors expect interest rates to decline in the future. They require a high short-term rate, perhaps because current inflation rates are high, but are willing to accept lower long-term rates due to the expected rate declines.
Why is the normal slope of the yield curve upward sloping to the right? a)Yields increase with time to reflect the increased risk of longer terms to maturity. b)Bond prices increase as the term to maturity of the bond increases. c)Yields are higher for bonds with shorter terms to maturity to compensate for the short holding period. d)Yields decrease as term to maturity increases.
a)Bond yields normally increase as the term to maturity increases to reflect the risk of holding a bond with a longer term. The actual slope of the yield curve can vary significantly depending on economic conditions and other factors such as supply and demand.
Sonoma is convinced that interest rates are going to drop. She wishes to buy a bond, hold it until rates have dropped, then sell it to earn a capital gain. Recommend a bond for her to purchase. a)A 6% 10 year bond. b)A 6% 8 year bond. c) A 6 month T-bill. d)9 month T-bill.
a)Longer-term bonds are more volatile in price than shorter-term bonds. If she wishes the price to move up more, she should choose the longer term bond.
What does the normal shape of the yield curve say about interest rates? a)Short-term rates are lower than long-term rates b)Long-term rates are lower than short-term rates c)Short-term and long-term rates are equal d)Medium-term rates are higher than short- and long-term rates
a)he normal shape suggests that short-term rates are lower than long-term rates. The most common shape for the yield curve is the normal curve. This shape occurs when long-term yields are higher than short-term yields and is thought to reflect the risk premium that investors require for holding longer term fixed-income securities.
What is the settlement period for Government of Canada bonds with terms to maturity of three years or less? a)Same day b)Second clearing day after the transaction takes place. c)Third clearing day after the transaction takes place. d)First clearing day on or after the fifteenth calendar day of the month.
b)Government of Canada (GoC) Treasury Bills are settled the same day. All GoC Bonds and GoC Guaranteed Bonds with a term to maturity of three years or less, or to the earliest call date, where a transaction is completed at a premium, are settled the second clearing day after the transaction takes place. All GoC Bonds and GoC Guaranteed bonds with terms to maturity of more than three years are settled the third clearing day after the transaction takes place.
Several theories have been developed to explain the shape of the yield curve: What are they explain each
--liquidity preference-Because there is greater interest rate risk associated with long-term bonds, investors generally prefer short-term bonds because of their liquidity. Investors will consider buying long-term bonds only if long-term yields are sufficient to compensate investors for the higher interest rate risk. --expectations-According to the expectations theory, investors' demand for higher yields on long-term maturities reflects their expectation of future short-term rates. For example, an investor should see no difference between investing in a 10-year bond or in a series of one-year bonds for 10 consecutive years — under the expectations theory, the return will be the same with either strategy. ---market segmentation-According to the market segmentation theory, investors have specific maturity preferences, thus short-term and long-term maturity ranges are distinct markets. For example, a financial institution may prefer the three- to seven-year maturity range when investing in bonds. The institution will move out of this preferred range, say to 10-year or longer-term maturities, only if there is a sufficient premium available on those securities.
What is the formula for calculating the Yield to Maturity (YTM) on a bond?
Interest Income +/- Annual price change * ------------------------------------------------------ x 100 (Purchase Price +100) ÷2 * annual price change is calculated as: Maturity Price - Purchase Price ---------------------------------------- # of compounding periods to maturity
What must an investor pay when purchasing a bond? a)The bond's market price plus interest accrued since the last interest payment. b)The market price of the bond. c)The market price of the bond as of the settlement date. d)The bond's market price less interest accrued since the last interest payment.
a)When a securities transaction takes place, the change in legal ownership of the securities is effective immediately. However, payment for purchased securities does not have to be made until some time later, and delivery of sold securities also does not have to be done until the end of this time period, called the settlement period. The length of the settlement period varies depending on the type of security being transacted. The client who purchases a bond pays the purchase or market price plus the interest which has accrued or accumulated since the last interest date. This interest is regained if the bond is held until the next interest payment date, or if the bond is sold in the meantime, resulting in accrued interest being paid to that seller.
You believe that the Bank of Canada will begin to tighten monetary conditions this year. According to the expectations theory, where would you expect long-term rates to be in relation to short-term rates? a)Higher than short-term rates b)Lower than short-term rates c)The same as short-term rates d)The expectations theory is not used to predict future interest rates
a)You would expect long-term rates to be higher than short-term rates. The expectations theory states that investors' demand for higher yields on long-term maturities reflects their expectation of rising future short-term rates. When the Bank of Canada tightens monetary conditions, short-term rates rise. Based on the expectations theory, investors will interpret this as an increase in future short-term interest rates.
If a financial institution has a preference for a specific maturity term sector, which of the following term structure theories is it following? a)Expectations theory b)Market segmentation theory c)Liquidity preference theory d)Rational expectations theory
b) A financial institution with a preference for a specific maturity term is adhering to the market segmentation theory. According to the market segmentation theory, investors have specific maturity preferences, thus short-term and long-term maturity ranges are distinct markets. For example, a financial institution may prefer the three- to seven-year maturity range when investing in bonds. The institution will move out of this preferred range, say to 10-year or longer-term maturities, only if there is a sufficient premium available on those securities.
The inflation rate is expected to be 3% next year. Sharif buys a bond at par with a 7% coupon. Calculate his real rate of return? a)3% b)4% c)7% d)10%
b)Because inflation reduces the value of a dollar, the return that is received, known as the nominal rate, must be reduced by the inflation rate to arrive at the actual or real rate of return. Real Rate = Nominal Rate - Inflation Rate.
If an investor expects market interest rates to decline, what type of bonds should she buy? a)Short-term, low coupon. b)Long-term, low coupon. c)Long-term, high coupon. d)Short-term, high coupon.
b)If market interest rates decline, bond prices will increase and bondholders will earn capital gains. The investor should attempt to maximize the potential capital gain by purchasing bonds that are more volatile. Long-term bonds are more volatile than short-term bonds and low coupon bonds are more volatile than high coupon bonds. Therefore, a long-term, low coupon bond offers the greatest potential for capital gains if interest rates decline.
DDD Co. Inc. has an outstanding 12 year bond with a coupon of 8.75%. The financial press is quoting it with a yield of 6%. What does this imply with respect to the bond? a)The price of the bond will be below par. b)The price of the bond will be at par. c)The price of the bond will be above par. d)The price of the bond will be slowing increasing to par as time to maturity approaches.
c)The most important bond pricing relationship to understand is the inverse relationship between bond prices and interest rates (or bond yields)— as interest rates rise, bond prices fall and as interest rates fall, bond prices rise. So if the yield of the bond has fallen below the coupon rate, the price must have increased above par.
Neta has read that interest rates are expected to go up. She currently owns 4 bonds and is thinking of selling one before this happens. Recommend a bond she should sell? a)A 6% 8 year bond with a duration of 7. b)A 7% 9 year bond with a duration of 8. c)5% 7 year bond with a duration of 6. d)A 6.5% 10 year bond with a duration of 9.
d)Duration is a measure of the sensitivity of a bond's price to changes in interest rates. It is defined as the approximate percentage change in the price or value of a bond for a 1% change in interest rates. The higher the duration of the bond, the more it will react to a change in interest rates. If interest rates are going up, prices will fall. She should sell the bond which is the most volatile as its price will fall the most. That is the bond with the highest duration.
JVV Inc. is about to sell a new issue of debt. The maturity of the debt is expected to be 20 years. Interest rates in the market place are as follows: Government of Canada 10 year bonds are yielding 4%. Government of Canada 20 year bonds are yielding 8%. 10 year corporate bonds are yielding 5%. 20 year corporate bonds are yielding 9%. What coupon rate should the company set for its new issue? a) 4% b)5 % c) 8% D)9%
d)The appropriate discount rate is chosen based on the risk of the particular bond. The discount rate can be estimated by the yields currently applicable to bonds with similar coupon, term and credit quality. These yields are determined by the marketplace and change as market conditions change. Companies would set the coupon rate on a new issue of bonds by determining what similar bonds are yielding.
Which of the following bond theorems are correct? i) Bond prices move inversely to interest rates. ii) The longer the term to maturity the greater the interest rate risk. iii) Bonds with low coupon rates have more price volatility than bonds with high coupon rates. iv) Bond prices are more volatile when interest rates are high. a)i) only. b)iv) only. c)ii), and iv) only d)i), ii), and iii).
d)There are some conventional rules regarding the price action of fixed-income securities. Each of these rules is explained separately below. First it must be understood that there is very little difference between interest rates and yields. After all, each represents a rate of return on an investment. Therefore, as interest rates rise, the yields on competing investments must also rise, and vice versa. Since interest payments are fixed, the only way to increase yields must be to decrease the market price, and vice versa. Bonds with long terms to maturity have more volatile prices i.e. when interest rates change, the price of longer term bonds change more than the price of shorter term bonds. Bonds with lower coupons have more volatile prices. When interest rates rise, bonds drop in price, but lower coupon bonds drop more than higher coupon bonds. This difference is material when larger coupon differences are considered, or when large sums of money are invested and even small price changes involve significant amounts of money. Bond prices are more volatile when interest rates are low. For example, a drop in yields from 12% to 10% will have a lesser impact on a bond's price than a drop in yields from 4% to 2%. Although both represent a drop of 200 basis points, or 2 percent, the former is a 17% change in yields, and the latter is a 50% change in yields. Thus, bond prices are more volatile when interest rates are low.
