Seres 66: Portfolio / Fixed Income Basics (Fixed Income Basics)
A $1,000 par TIPS is issued with 5 years to maturity. The coupon rate on the bond is 3.50%. If the inflation rate for the next 5 years is 2.50%, the bond will be worth how much in 5 years?
$1,131 A TIPS is a Treasury Inflation Protection Security. Aside from receiving the 3.50% coupon ($35 annual interest) paid to the bondholder, the principal is adjusted upwards by the inflation rate each year, and at maturity, the holder receives the inflated principal amount. $1,000 inflated by 2.50% annually equals: $1,000 x 1.025 x 1.025 x 1.025 x 1.025 x 1.025 = $1,131. (Note, while in reality the principal gets adjusted semi-annually, to simplify the calculation, we are adjusting the principal annually.)
In 2020, a customer buys 5 ABCD 10% debentures, M '49, at 85. The interest payment dates are Feb 1st and Aug 1st. The bonds are callable as of 2025 at 103. The current yield on the bonds is:
11.76% The formula for current yield is: annual interest / bond MP = current yield $100$850=11.76%
A customer wishes to sell shares of her S&P 500 Index Fund and use the sale proceeds to purchase a non-callable agency bond. Which risk is NOT associated with this transaction?
Prepayment risk The purchase of a fixed income bond means that the investment will have interest rate risk - if market interest rates rise, the price of the bond will fall. Any long-term fixed income investment has purchasing power (inflation risk). If prices are rising due to inflation, the fixed payments received over many years become less and less valuable because of inflation. Opportunity cost risk is the risk that making an alternative investment would have yielded a better return - this risk is inherent to any investment decision. There is no prepayment risk for a non-callable bond - the bond cannot be called (prepaid) early by the issuer if market interest rates fall. If the bond were callable, then this risk would be present.
The cost of money is known as the:
interest rate The interest rate charged on loans is the "cost" of money. The higher the interest rate, the higher the "cost" of borrowing money, and vice-versa.
The closest approximation of the internal rate of return on a bond is the bond's:
yield to maturity The internal rate of return on a bond is the interest rate that will discount the bond's cash flows to the purchase price of the bond. It is the same as the bond's yield to maturity.
A $1,000 par bond is issued with 3 years to maturity. The coupon rate on the bond is 2.50%. If the inflation rate for the next 3 years is 1.50%, the bond will be worth how much in 3 years?
$1,000 The bond matures in 3 years. At maturity, the bondholder receives par from the issuer. The 2.50% coupon ($25 in interest) is paid to the bondholder annually, divided into semi-annual payments. The inflation rate has nothing to do with this question.
A yield quote change of 5 basis points on municipal bonds with a 6.25% nominal yield will result in the greatest dollar price change for bonds quoted at:
8.50% with 4 1/2 years to maturity All of the bonds listed are discount bonds (the only way for the yield to be higher than the fixed coupon rate is for the bond to be selling at a discount). As a general rule, the deeper the discount, the more volatile the bond's price movements in response to market interest rate changes. Also, the longer the maturity, the more volatile the bond's price movements in response to market interest rate changes. The 6.25% bond quoted on an 8.50% yield with 4 1/2 years to maturity has both the longest maturity and deepest discount. This bond's price will move the farthest in response to market interest rate changes.
Which bond will decrease the most in price, if interest rates rise by 50 basis points?
A bond with high duration Duration is a measure of bond price volatility. Bonds with low coupons have large duration numbers; as do bonds with long maturities. Thus, the bonds with the biggest durations are those that are most volatile in price.
What rate would be used to find the present value of a TIPS?
Coupon Rate of TIPS Finding the present value of a TIPS (Treasury Inflation Protection Security) is the same thing as calculating the market price of a TIPS using discounted cash flows. The coupon rate on a TIPS is the interest rate at issuance that will price the instrument at par. Assume that this interest rate is 2% for a 30 year TIPS. If there is no inflation, the annual cash flow received for each of the next 29 years will be 2% of $1,000 = $20; and in year 30, the customer will receive $1,020 ($1,000 principal without any inflation adjustment plus another $20 of interest). If these cash flows are discounted at the coupon rate of 2%, the price of the bond will be par. If there is inflation, then the principal amount is adjusted upwards in that year for the CPI increase, and the cash flow received in that year also increases, since the 2% coupon is applied against the increased principal amount. Because the cash flows are increasing due to inflation, when they are discounted at the 2% coupon rate, this means that the bond will be valued above par. Conversely, if there is deflation, then the principal amount is adjusted downwards in that year for the CPI decrease, and the cash flow received in that year also decreases, since the 2% coupon is applied against the decreased principal amount. Because the cash flows are decreasing due to deflation, when they are discounted at the 2% coupon rate, this means that the bond will be valued below par.
When making a recommendation of corporate commercial paper to a customer, which risk is the MOST important consideration?
Credit risk Credit risk is the risk that the issuer cannot make interest and principal payments as due. Since Commercial Paper is unsecured, investors are buying a security backed only by "faith and credit" - so credit quality is the major consideration. Because commercial paper is short term, there is minimal purchasing power risk and market risk. Over a short term time horizon, short term interest rates cannot rise much. Commercial Paper, like all money market instruments, is non-callable so this risk is not a factor.
Which statements are TRUE when a bond sells at a discount? I The nominal yield is less than the yield to maturity II The nominal yield is more than the yield to maturity III The current yield is less than the yield to maturity IV The current yield is more than the yield to maturity
I and III This one is worded in a tricky manner. For discount bonds, the relationship of yields from highest to lowest is: Yield to Maturity (Highest) Current Yield Nominal Yield (Lowest) Therefore, nominal yield is lower than current yield (Choice I) and current yield is lower than yield to maturity (Choice III). Yield to maturity is highest for a discount bond because it reflects both the fact that the bond was purchased for less than par and that the discount will be earned over the life of the bond. Current yield only reflects the fact that the bond was purchased for less than par; it does not include the annual earning of the discount. Finally, nominal yield is the yield based on purchasing the bond at its original par value - it is the lowest yield of the choices offered because it neither reflects the discount price nor the annual accretion of that discount.
A blue chip corporation is making a bond offering that is rated AAA. During the issue's first year of trading, what is the greatest potential risk that a bondholder assumes?
Interest rate risk Because this is a bond offering that is rated AAA, it will be highly marketable. The bond will be easy to sell, so marketability risk is minimal. Liquidity risk is closely aligned with marketability risk. It is the risk that selling will incur high transaction costs, which is typical of illiquid investments. That is not the case with a AAA-rated bond. So we are left with either inflation risk or interest rate risk as the correct answer. Most corporate bond issues are 30-year bonds. If this is the bond's first year of trading, it probably has 29 years of life left. If market interest rates rise (which is typical in an expanding economy), long-term bonds are impacted more than short term bonds, and their price will fall dramatically. This is the greatest potential risk. The risk of inflation is also very real because it leads to higher interest rates, but this is generally a slower moving phenomenon than rising interest rate levels in an improving economy.
A trader maintains a position in a small capitalization stock that has low trading volume. The trader has a high level of:
Liquidity risk The best of the choices is that this trader is taking on liquidity risk. This is a thinly traded stock that will be hard to sell in any quantity without adversely affecting the price for that issue. There is also a relatively high level of business risk, but since the question emphasizes that low trading volume of this issue, liquidity risk is the better choice.
An investor believes that interest rates will be flat or falling into the future; and that prices may deflate. The MOST appropriate investment is:
Long term U.S. Government bonds In periods of deflation, interest rates fall. A fixed income security's price will go up as interest rates fall. Furthermore, since prices are deflating, the fixed interest payments received are able to buy more and more over time. This is the best investment choice. In times of deflation, real estate prices fall; as do gold prices. Stock prices tend to fall as well, since companies are forced to cut their prices to maintain sales volume.
For bonds trading at a discount, rank the yield measures from lowest to highest?
Nominal; Current; Yield to Maturity; Yield to Call When bonds are trading at a discount, the stated (nominal) yield will be lowest. The current yield will be higher, since it is based on the discounted market price - not par value. The yield to maturity will be the next highest, since it includes the portion of the discount earned annually as part of the annual return in addition to the interest received. Finally, yield to call will be highest, since the discount would be earned over a shorter period of time, increasing the annual yield on the security.
A customer who is concerned with social and environmental issues would minimize which risk when making an investment decision?
Regulatory This customer believes in socially responsible investing, and thus would avoid companies such as tobacco, alcohol, fossil fuels, etc. These are companies that are under increasing regulatory pressure, and more stringent regulation is "regulatory risk." Financial risk is simply the risk that a company goes bankrupt. Market risk is the risk that the market falls, taking all stocks with it. There is no such thing as Opportunity Risk - rather there is Opportunity Cost - which is the amount of an investment return that is not earned when an inferior investment is chosen.
Given the formula: X =Municipal Yield / 1 - Tax Bracket % X is equal to the:
Taxable Equivalent Yield The formula for the Taxable Equivalent Yield is: Tax-Free Yield / 100% - Tax Bracket % = Taxable Equivalent Yield For example, if a customer is in the 30% tax bracket, and can purchase a municipal tax-free bond yielding 7%, this is the same as earning 10% on a taxable investment. Tax-Free Yield / 100% - Tax Bracket % 7% / 1 - .3 = 7%. / 7 = 10% Because the 30% of the 10% earned on a taxable investment will go to pay taxes, there is 7% left "after-tax." A non-taxable municipal bond yielding 7% gives the equivalent return.
Over the past 4 years, a customer's fixed income portfolio value has dropped by 2%. During the same period, the Consumer Price Index has dropped by 5%. Based on these facts, which statement is TRUE?
The customer's purchasing power has increased The customer's portfolio value has dropped by 2%; and prices have dropped by 5%; so this customer is gaining purchasing power. If prices are falling faster than the portfolio value, then each $1 in the portfolio can buy proportionately more.
Years ago, a bond was issued at par with a 7% coupon. This year, new issue bonds of similar credit quality are being issued at 10%. Which statement is TRUE?
The new bonds will be issued at a premium to the current price of the 7% bonds Because interest rates have risen from 7% to 10%, any new issue bonds will come out at par with a 10% coupon; while the prices of outstanding bonds with lower coupons will drop in the market. Thus, new bonds will be selling at a premium to the current price of existing bonds that have lower coupons.
A customer wishes to make an investment that provides liquidity, marketability and current income. The BEST recommendation is:
Treasury Note This customer is looking for current income, so growth stocks are inappropriate. This customer is looking for ready marketability and CDs are not very marketable - they are typically held to maturity. Both preferred stock and Treasury notes provide current income, but Treasuries are more marketable and more liquid. This is the best of the choices offered.
A customer who is retired wants to select an investment that is liquid, marketable, and that provides regular income. The BEST choice would be to recommend:
Treasury Notes Certificates of Deposit are non-negotiable - they are non-marketable, so this does not meet the client's needs. Preferred stock is marketable, but not as marketable as Treasury securities, making Treasury securities the better choice. So we are left with either a T-Bill or a T-Note. Treasury notes pay interest semi-annually; while Treasury Bills do not provide a regular income stream, so a T-Note is the better choice. (One could argue that buying T-Bills at a discount and letting them mature at par and then rolling over the original investment amount into a new T-Bill purchase will also provide an income stream, but this requires continuous reinvestment on the part of the customer. Buying a T-Note is a completely passive investment in terms of the customer's needs.)
An investor buys a $100,000, 10% corporate bond maturing in 2030 for $125,000. The bond is callable starting in the year 2020. What is the most appropriate measure for calculating yield?
Yield to Call This investor is paying $125,000 for a 10% bond with a face value of $100,000. Thus, the investor is paying a 25% premium for the bond. If the bond is called prior to maturity (which is very likely, since current market interest rates must be lower than the coupon rate, otherwise the bond would not be trading at a premium, and the issuer, by calling in the bond, can refinance the issue at lower current market rates), then the premium will be lost more quickly than if the bond were held to maturity, reducing the effective yield. Thus, this bond's yield to call will be lower than yield to maturity. Furthermore, this bond is likely to be called, so using the call date is the appropriate time frame for computing the yield for this bond. By the way, this is a tough question! Review
The yield to maturity on a bond is less than the yield to call. This bond is trading:
at a discount Aside from the coupon rate earned on a bond, yield to maturity and yield to call computations take into account whether the bond is purchased at a discount or at a premium. If a bond is purchased at a discount, the pro-rata annual earning of the discount as the bond approaches par value at maturity is added to the coupon rate, increasing the yield. If such a bond is called prior to maturity (an unlikely event), then the discount is earned faster and the yield to the "call date" increases above the yield to maturity. Thus, for a discount bond, the yield to maturity is lower than the yield to call.
An investor who places the majority of assets in a single stock exposes the portfolio to:
business risk Business risk is the risk that a specific issuer performs poorly due to business conditions - and its securities decline in price because of this. If a majority of a portfolio is in one stock, then the portfolio is highly exposed to this risk. As more and more stocks are added to the portfolio, this risk is diversified away. Once a portfolio is fully diversified, the only risk left is market risk - the risk that there is a general decline in the market; and all stocks fall as a result.
When borrowing money, the interest rate charged measures the:
cost of money The interest rate charged on loans is the "cost" of money. The higher the interest rate, the higher the "cost" of borrowing money, and vice-versa.
A 7% coupon bond is being offered on an 8% basis. If interest rates for similar bonds fall below 8%, the basis for this bond will:
decrease This is pretty simple. A basis quote is a yield to maturity quote. If market yields are rising, the basis quote will rise, forcing the bond's price down. If market yields are falling, the basis quote will fall, forcing the bond's price up.
During periods when interest rates are rising, which of the following fixed income securities offers the greatest protection from "interest rate risk"?
high coupon bonds with long maturities The basic truths regarding bond price volatility and interest rate movements are: The longer the maturity, the greater the bond's price volatility in response to interest rate movements. The lower the coupon rate, the greater the bond's price volatility in response to interest rate movements. The farther away from par that the bond is priced, the greater the bond's price volatility in response to interest rate movements. This question only examines the second factor, since the maturities are equivalent for all choices, and no mention is made of whether the bonds are trading at a discount or a premium. The bond with the lowest price volatility will be the one with the highest coupon rate. Bonds with low coupon rates exhibit greater price volatility. Thus, to minimize price volatility due to interest rate movements ("interest rate risk"), high coupon bonds are appropriate.
The quantitative method of evaluating investments that finds the interest rate that discounts periodic cash inflows and outflows to a present value of "0" is:
internal rate of return The internal rate of return of an investment is the implicit interest rate that discounts the cash flows generated by the investment to a value of "0." This is the true "yield" of the investment, considering the time value of money.
The risk of tax law changes that may negatively affect securities held in a portfolio is called:
legislative risk Legislative (regulatory) risk is the risk of law changes; primarily the risk of tax law changes. Since the interest income from municipal bonds is exempt from Federal income tax, the main risk associated with these securities is that the Federal government may attempt to tax their interest income (this has already happened with certain types of municipal bonds). Also note that these securities are subject to market risk and credit risk; but this is not the "primary" concern with these investments.
Which of the following risks is the primary concern when investing in a municipal bond?
legislative risk Legislative (regulatory) risk is the risk of law changes; primarily the risk of tax law changes. Since the interest income from municipal bonds is exempt from Federal income tax, the main risk associated with these securities is that the Federal government may attempt to tax their interest income (this has already happened with certain types of municipal bonds). Also note that these securities are subject to purchasing power risk, market risk, and credit risk; but this is not the "primary" concern with these investments.
A retired married customer, age 73, has a portfolio that is invested in Blue Chip stocks and Treasury bonds that provides current income. The customer is concerned that he is paying a very high Federal and State combined income tax rate. An appropriate recommendation for this customer would be to diversify part of his portfolio into an investment in:
municipal bonds This customer is concerned about paying a high Federal income tax rate and a high State income tax rate. By purchasing municipal bonds of his State of residence, the income from those bonds would be free of Federal, State and Local income taxes. This customer is too old to be able to contribute to tax-qualified retirement plans (the cut-off is age 72), making choice A incorrect. Note that the customer could buy a non-tax qualified annuity, but the income from the annuity would be taxable anyway. The income from securities held in offshore accounts must still be reported on the customer's U.S. tax return and taxes paid in the U.S. on that income. Finally, the income from promissory notes is fully taxable at the Federal and State levels.
A 20-year, 5% bond is quoted by a dealer on a 6% basis. The bond is callable in 10 years at par. To calculate the dollar price for the bond, the dealer would use the:
redemption date to find the number of years over which the discount would be earned This is a discount bond. To approximate the price for a long-term bond, divide the coupon by the basis = 5/6 x $1,000 par = $833. A discount bond is one that the issuer would not call - because market interest rates have risen. To bring a 5% coupon up to a 6% yield implies that 1% will be earned each year = 1% of $1,000 = $10 annual earning of discount. If the bond were called early (not likely), the discount would be earned faster and the customer would get a higher yield than the 6% promised. The worst case scenario for the customer is the bond being held to maturity. If it were called early, the yield would actually improve. For bonds quoted on a yield basis, dealers must use "yield to worst" pricing. For discount bonds, this is the case if the bond is held to maturity - this is where the discount would be earned at the slowest rate.
Bond A and Bond B both have an 8% coupon. Bond A matures in 2 years, while Bond B matures in 10 years. If market interest rates rise:
the price of Bond B will fall faster than the price of Bond A As market interest rates rise, the prices of fixed income securities fall, but not at equal rates. As market interest rates rise, the longer the maturity of the bond, the faster the price will fall; and the lower the coupon rate, the faster the price of the bond will fall. Since the coupon is the same for both bonds, the price of the longer maturity bond (B) will fall faster as market interest rates rise.
A TIPS is issued with a 3.5% coupon rate and a 5 year maturity. If inflation runs at 4% per year for the 5-year life of the bond, the redemption value of the bond at maturity will be approximately:
$1,219 TIPS are Treasury Inflation Protection Securities. The bonds are issued at par with a lower interest rate than conventional Treasury bonds. In return, the principal amount is adjusted upwards for inflation, with the inflated principal amount paid at maturity. The inflation adjustment is made semi-annually when the interest payment is made. Thus, if inflation runs at 4% annually for the 5-year life of the bond, the principal amount will have been adjusted upwards 10 times, at a 2% increase per adjustment.After the 1st year, the bond's value is $1,000 x 1.02 x 1.02 = $1,040.40After the 2nd year, the bond's value is $1,040.40 x 1.02 x 1.02 = $1,082.43After the 3rd year, the bond's value is $1,082.43 x 1.02 x 1.02 = $1,126.16After the 4th year, the bond's value is $1,126.16 x 1.02 x 1.02 = $1,171.66After the 5th year, the bond's value is $1,171.66 x 1.02 x 1.02 = $1,218.99
A customer has the choice of investing $20,000 in a risk free investment yielding 3% per year; or can invest the money in a growth mutual fund that has returned 10% per year over the past 3 years and can reasonably be expected to produce a similar return in the future. What is the customer's annual opportunity cost if he or she chooses the risk free investment?
$1,400 This customer has the choice of earning 3% per year risk free; or earning 10% per year by taking on a higher level of risk. If the customer chooses the risk free investment, the customer gives up 7% per year (the "opportunity cost" of the investment). 7% x $20,000 investment = $1,400 annual opportunity cost. (Also note that past performance of a mutual fund cannot be used to predict future performance, but that is not what this question is going after!)
Investment A requires a $15,000 initial investment with a 3 year investment time horizon. It is expected to generate $4,000 of positive cash flow in Year 1, $6,000 of positive cash flow in Year 2, and $8,000 of positive cash flow in Year 3. Assuming that the market rate of return for investments of similar risk and investment time horizon is 10%, the NPV of this investment is:
-$394.44 Net Present Value takes the cash flows from an investment and discounts them back to today's present value. The "Net" part of the formula, is that the initial investment outlay ($15,000 in this case) is deducted from the present value of the positive future cash flows. If the NPV is positive, this is a good investment. In this example, in Year 0, -$15,000 is the initial cash outlay. At the end of Year 1, $4,000 of cash flow is received, discounted to today's present value using the 10% market rate of return = $4,000/1.10 = $3,636.36. At the end of Year 2, $6,000 of cash flow is received, discounted to today's present value using the 10% market rate of return = $6,000/(1.10 x 1.10) = $4,958.68. At the end of Year 3, $8,000 of cash flow is received, discounted to today's present value using the 10% market rate of return = $8,000/(1.10 x 1.10 x 1.10) = $6,010.52. The NPV is -$15,000 + $3,636.36 + $4,958.68 + $6,010.52 = -$394.44 Because the NPV is negative, this indicates that the investment is generating a lower return than the market rate of return for similar investments and that the investment should not be made.
Investment A requires a $13,000 initial investment with a 3 year investment time horizon. It is expected to generate $5,000 of positive cash flow in Year 1, $5,000 of positive cash flow in Year 2, and $5,000 of positive cash flow in Year 3. Assuming that the market rate of return for investments of similar risk and investment time horizon is 10%, the NPV of this investment is:
-$565.75 Net Present Value takes the cash flows from an investment and discounts them back to today's present value. The "Net" part of the formula, is that the initial investment outlay ($13,000 in this case) is deducted from the present value of the positive future cash flows. If the NPV is positive, this is a good investment. In this example, in Year 0, -$13,000 is the initial cash outlay. At the end of Year 1, $5,000 of cash flow is received, discounted to today's present value using the 10% market rate of return = $5,000/1.10 = $4,545.45. At the end of Year 2, $5,000 of cash flow is received, discounted to today's present value using the 10% market rate of return = $5,000/(1.10 x 1.10) = $4,132.23. At the end of Year 3, $5,000 of cash flow is received, discounted to today's present value using the 10% market rate of return = $5,000/(1.10 x 1.10 x 1.10) = $3,756.57. The NPV is -$13,000 + $4,545.45 + $4,132.23 + $3,756.57 = -$565.75 Because the NPV is negative, this indicates that the investment is generating a lower return than the market rate of return for similar investments and that the investment should not be made.
A customer has a 10-year investment time horizon and has $5,000 available for investment each year over that time frame. The customer wishes to have $100,000 at the end of that time. In order to accumulate $100,000 at the end of 10 years, the approximate rate of return on investment would need to be:
12% There are a number of ways to deal with this question. This customer is investing $5,000 a year in each of the next 10 years, for a total investment of $50,000. Using the "Rule of 72" dividing the Rate of Return into 72 gives the approximate number of years needed for an investment to double. Thus, if an investment is returning 7.2% (72/7.2), it would double in 10 years. However, all $50,000 is not being invested in the first year - rather, it is being invested at the rate of $5,000 per year over 10 years, for an average aggregate investment value of $25,000 ($50,000/2) over the 10 years. For $25,000 to become $100,000 over 10 years, it must double to $50,000 and double again to $100,000. Thus, the approximate rate of return would need to be double 7.2% = 14.4%. But it would be a bit lower than this, since any earnings are compounding at a much higher interest rate than 7.2%. Of the 4 choices offered, the highest is 12% - all the other choices are lower - so this must be the answer. Another way of proving this is to do the math: $5,000 invested for 10 years at 12% would be worth $5,000 x (1.12)10 = $15,529 10 years out $5,000 invested for 9 years at 12% would be worth $5,000 x (1.12)9 = $13,865 9 years out $5,000 invested for 8 years at 12% would be worth $5,000 x (1.12)8 = $12,380 8 years out $5,000 invested for 7 years at 12% would be worth $5,000 x (1.12)7 = $11,053 7 years out $5,000 invested for 6 years at 12% would be worth $5,000 x (1.12)6 = $9,869 6 years out $5,000 invested for 5 years at 12% would be worth $5,000 x (1.12)5 = $8,812 5 years out $5,000 invested for 4 years at 12% would be worth $5,000 x (1.12)4 = $7,868 4 years out $5,000 invested for 3 years at 12% would be worth $5,000 x (1.12)3 = $7,025 3 years out $5,000 invested for 2 years at 12% would be worth $5,000 x (1.12)2 = $6,272 2 years out $5,000 invested for 1 year at 12% would be worth $5,000 x (1.12) = $5,600 1 year out Adding up the future values: $98,273 This is a lot of work to do to answer a question. Since the 4 choices are so far apart, using the "approximate" method is just fine.
A customer has purchased three different bonds, each yielding 9%, with 5 year, 10 year, and 15 year maturities. If prevailing interest rates drop by 20 basis points, which will show the greatest percentage price change?
15 year maturity As interest rates move, long term maturities will change in price at a faster rate than will short term obligations. This is due to the fact that the "compounding effect" is more acute as maturities lengthen. As interest rates move up, long term maturities fall faster in price than do short-term maturities.
A customer invests $1,000 over a 10 year time horizon. At the end of 10 years, the investment is worth $4,000. The compounded annual rate of return is approximately:
15% Since financial calculators are not provided on the test, the mathematically correct way to do this problem is not available. The "correct" way is to find the interest rate that discounts $4,000 to be received 10 years from now to $1,000 invested today. This is the "IRR" or Internal Rate of Return. But since you only have a simple calculator to use, the "eyeball" method is best, testing each of the 4 choices. Just by looking at the 4 choices, earning either a 150% or 300% compounded rate of return is ridiculous. Either of these would produce enormous gains over 10 years, so Choices C and D are clearly wrong. So let's take Choice A, which is 15%. If we invest $1,000 today, and the investment grows at 15% per year: After 1 year, the investment is worth $1,000 x 1.15 = $1,150.00 After 2 years, the investment is worth $1,150 x 1.15 = $1,322.50 After 3 years, the investment is worth $1,322.50 x 1.15 = $1,520.875 After 4 years, the investment is worth $1,520.875 x 1.15 = $1,749.0062 After 5 years, the investment is worth $1,749.0062 x 1.15 = $2,011.3571 After 6 years, the investment is worth $2,011.3571 x 1.15 = $2,313.0606 After 7 years, the investment is worth $2,313.0606 x 1.15 = $2,660.0196 After 8 years, the investment is worth $2,660.0196 x 1.15 = $3,059.0224 After 9 years, the investment is worth $3,059.0224 x 1.15 = $3,517.8757 After 10 years, the investment is worth $3,517.8757 x 1.15 = $4,045.5571 This is the answer. Another (simpler) way of approximating the answer is to use the Rule of 72, which calculates how many years it takes for an investment value to double. If $1,000 is invested today, it must double to $2,000 in value and then double again to $4,000 in value within 10 years. 72 / 10 years = 7.2% yield for the investment value to double from $1,000 to $2,000. Since this amount doubles again to $4,000 within that time frame, double 7.2% = 14.40% (approximate) yield. There is only 1 choice offered that is even close to this result, 15% which is Choice A.
A 20-year Zero-Coupon Treasury bond has a duration of:
20 Duration is the number of years until the $1,000 par principal of a bond is paid back. Since a zero-coupon bond makes no interest payments, the entire $1,000 par principal amount is paid back at the maturity date, making the duration of a 20-year zero coupon bond equal to 20.
A customer buys a 2-year maturity, 10% coupon bond at par. If market interest rates rise to 12%, then the bond's price will fall by approximately:
3.4% The customer bought this 2-year bond at par with a coupon rate of 10%. If market interest rates rise to 12%, then the present value of the bond's cash flows will fall as follows (rounded): Year 1:$100 / 1.12 = $89.29Year 2:$1,100 / (1.12)2 = $876.91 Total Present Value = $89.29 + $876.91 = $966.20 The bond will fall in price by $33.80 from $1,000 par, for a fall of 3.4%.
What happens to the rate of return calculation on a non-callable bond if the rate of interest stays the same and the time intervals are changed? I Shortening the time intervals will increase the rate of return II Shortening the time intervals will decrease the rate of return III Lengthening the time intervals will increase the rate of return IV Lengthening the time intervals will decrease the rate of return
I and IV When the question is stating that the "time intervals shorten," this means that the time period between each interest payment received shortens. When the question is stating that the "time intervals lengthen," this means that the time period between each interest payment received lengthens.For example, assume that a 10% bond will pay interest semi-annually, instead of annually. At the end of each 6 months, $50 of interest will be received, instead of receiving $100 every 12 months. Because the first $50 interest payment received can immediately be reinvested over the next 6 months until the second $50 payment is received, this will produce a higher rate of return than receiving the $100 payment at the end of the year. Thus, the actual rate of return will increase if time intervals shorten, because the interest is actually being received more quickly, and can be reinvested faster, increasing the rate of return. Conversely, if the time intervals lengthen, because the actual interest payments are being received more slowly and are reinvested more slowly, the rate of return declines.
If a bond is purchased at a premium, which of the following statements are TRUE? I Yield to call is higher than the yield to maturity II Yield to call is lower than the yield to maturity III Yield to maturity is higher than the current yield IV Yield to maturity is lower than the current yield
II and IV When a bond is purchased at a premium and called prior to its maturity date, the yield to call received will be lower than if the bond is held to maturity since the premium will be lost faster. Yield to maturity will always be lower than current yield for a premium bond because YTM includes the loss of the premium as a reduction of the overall return received from the bond; while current yield ignores this component (it is simply Annual Income / Current Market Price).
Exchange rate risk is a factor to consider when investing in debt issues: I within the U.S. II outside the U.S. III that are denominated in U.S. dollars IV that are denominated in a foreign currency
II and IV When an investment is made outside the U.S. that is denominated in a foreign currency, the investor assumes exchange rate risk. This is the risk that the foreign currency weakens against the U.S. dollar (which is the same as the U.S. dollar strengthening). For example, assume that an investment is made in $100,000 of bonds denominated in Japanese Yen when the Yen is trading at 100 to the U.S. dollar. Thus, $100,000 x 100 Yen per U.S. dollar = 1,000,000 Yen being spent. Also assume that each bond costs 10,000 Yen, so 100 bonds are purchased at $100 each. Now assume that the bonds do not move in price, but the Yen weakens to 200 Yen to the U.S. dollar (each U.S. dollar now "buys" 200 Yen instead of 100 Yen). This means that 100 bonds are still priced at 10,000 Yen each in Japan. However, because each U.S. dollar is worth 200 Yen, the bonds are now worth 10,000 Yen / 200 Yen per U.S. dollar = $50 each. Thus, the bonds are now worth 1/2 of what was paid for them, solely due to the movement in currency exchange rates.
2 years ago a woman leased a new car by putting $2,000 down and signing a 48 month lease at $500 per month. She has received a letter from the lease company saying that she can complete the lease right now by making a single $10,000 payment and keep the car for 2 more years; or she can finish the lease by making the remaining 24 monthly payments of $500. Assuming that this customer can earn 6% by investing in Treasury securities, and ignoring any tax consequences, to determine the best option, the method to be used is:
Net Present Value This customer can get out of the lease by making a $10,000 payment now; or can continue to make $500 per month payments for the next 24 months, paying a total of $12,000 to complete the lease. One method to compute the best option (lowest cost) would be to use net present value. The customer can pay off the lease now by paying $10,000 now - this is the present value of this payment. Using NPV and a 6% risk-free rate of return, the present value of continuing the lease payments is: $6,000 paid in 1 year1.06= $5,660 NPV for year 1 payments $6,000 paid in 2 years1.06(2)= $5,340 NPV for year 2 payments Total NPV = $5,660 + $5,340 = $11,000 Paying off the lease in one payment costs $10,000; while the net present cost of continuing the lease is $11,000. The up-front $10,000 payment is the best alternative (assuming that the customer has the $10,000 on hand!).
An investor that buys securities issued by companies based in Third World countries would be MOST concerned with:
Political risk Investing in any Third World country is risky. The major risk of investing in a Third World country is political risk. For example, the country changes its laws and "nationalizes" your private investment - without compensating you! Currency exchange risk is always an issue with a foreign investment, but it typically is not a risk that will bankrupt an investor. Any security can have purchasing power risk - the risk that inflation devalues your investment's value. Finally, any fixed income security has interest rate risk - the risk that if market interest rates rise, the value of the fixed income security will fall.
Which recommendation is suitable for an investor who believes that the economy will experience an extended period of inertial inflation?
Real Estate Inertial inflation is inflation that is contractually embedded in the economy. For example, COLAs (Cost of Living Adjustments) in union and government employment contracts are tied to increases in the inflation rate. Inertial inflation can be "self-fulfilling" because as wages rise due to COLAs, this creates inflationary pressure on prices of goods and services, so their prices rise, which triggers another COLA increase, etc. In periods of sustained inflation, bonds do terribly because interest rates rise, and stocks don't fare well either. Tangible assets such as real estate are the best investments in periods of sustained inflation.
What rate would be used to find the present value of a TIPS?
Real Rate of Return at the time the bond was issued Finding the present value of a TIPS (Treasury Inflation Protection Security) is the same thing as calculating the market price of a TIPS using discounted cash flows. The coupon rate on a TIPS is the interest rate at issuance that will price the instrument at par. This is the same as the "real rate" of return at that point in time (the real rate has the current inflation deducted out, because there is no "inflation risk" on a TIPS). Assume that the 30-year Treasury Bond is issued with a 3% coupon rate when the inflation rate is 1%. The "real" rate of return is 2%, and this would be the interest rate on a 30-year TIPS issued at that time. Assuming that this interest rate is 2% for a 30 year TIPS. If there is no inflation, the annual cash flow received for each of the next 29 years will be 2% of $1,000 = $20; and in year 30, the customer will receive $1,020 ($1,000 principal without any inflation adjustment plus another $20 of interest). If these cash flows are discounted at the coupon rate of 2%, the price of the bond will be par. If there is inflation, then the principal amount is adjusted upwards in that year for the CPI increase, and the cash flow received in that year also increases, since the 2% coupon is applied against the increased principal amount. Because the cash flows are increasing due to inflation, when they are discounted at the 2% coupon rate, this means that the bond will be valued above par. Conversely, if there is deflation, then the principal amount is adjusted downwards in that year for the CPI decrease, and the cash flow received in that year also decreases, since the 2% coupon is applied against the decreased principal amount. Because the cash flows are decreasing due to deflation, when they are discounted at the 2% coupon rate, this means that the bond will be valued below par.
When prices in an economy are adjusted with relation to a price index by force of contract, this is called:
inertial inflation Inertial inflation is inflation that is contractually embedded in the economy. For example, COLAs (Cost of Living Adjustments) in union and government employment contracts are tied to increases in the inflation rate. Inertial inflation can be "self-fulfilling" because as wages rise due to COLAs, this creates inflationary pressure on prices of goods and services, so their prices rise, which triggers another COLA increase, etc. In periods of sustained inflation, bonds do terribly because interest rates rise, and stocks don't fare well either. Tangible assets such as real estate are the best investments in periods of sustained inflation.
If the market rate of interest is 10%, the net present value of $1,000 to be received 2 years from now is:
less than $1,000 The net present value of $1,000 to be received 2 years from now, given that the market rate of interest is 10%, is $1,000 / 1.21 (which is 1.1 x 1.1, considering that interest is compounding at a 10% rate for 2 years) = $826.44. Another way of looking at this is that $826.44 received today will be worth $1,000 2 years from now, if it is invested at a 10% rate of return. $826.44 x 1.1 = $909.09 value after 1 year $909.09 x 1.1 = $1,000 value after 2 years
The primary risk associated with investing in an index fund is:
market risk Index funds are fully diversified - so business risk is minimized. There is little liquidity risk because index fund shares can be redeemed at Net Asset Value daily. Diversification does not protect against market risk. If the market falls in general, so will the value of the securities in the index fund. Market risk is the risk that cannot be diversified away (but one can hedge against it by using the appropriate option contract).
The effect on the prices of securities due to the "changing tastes, likes and dislikes" of investors is:
market risk Is this one special or not?! When investors like stocks, they buy them and stock prices rise. When investors don't like stocks, they either sell them or don't buy them and prices fall. This is market risk. Business risk is the risk that a negative event, bad management or bad products cause a company to become unprofitable. Regulatory risk is the risk of law change negatively affecting a company's operations. Opportunity cost is the return "lost" by making a suboptimal investment
Equity investments fall out of favor with investors due to a period of steep economic decline and stock prices fall broadly. This is an example of:
market risk When investors like stocks, they buy them and stock prices rise. When investors don't like stocks, they either sell them or don't buy them and prices fall. This is market risk. Business risk is the risk that a negative event, bad management or bad products cause a company to become unprofitable. There are no investment-related risks that are called cyclical risk or economic risk.
The risk that is unique to mortgage backed securities is:
prepayment risk Mortgage backed securities pass through the monthly mortgage payments to the certificate holders. Because the homeowners have the right to prepay their mortgages without penalty, when market interest rates drop, the homeowners refinance their mortgages, and these early principal repayments are passed-through to the certificate holders. Thus, the certificates pay off much earlier than expected as the expected maturity shortens (this is also called contraction risk). The certificate holders that receive the early principal payments will now have to reinvest them in new MBSs, which will be yielding less because market interest rates have declined. All securities have credit risk (risk of default) with the possible exception of U.S. Government debt (the safest debt in the world and credit risk-free for test purposes). All fixed rate securities have interest rate risk (the risk of rising interest rates forcing the value of outstanding lower-rate issue downwards to bring their yields up to current market rates) and purchasing power risk (inflation risk, which will increase interest rates and depress bond prices).
An investor that purchases 10 year zero-coupon Treasury bonds with the intention of holding them to maturity should be MOST concerned with:
purchasing power risk Market risk (which is the same as interest rate risk for bonds) is the risk that market interest rates rise, forcing bond prices down. This is a major issue for zero-coupon bonds, but it is not an issue if the investor is holding them to maturity. At maturity, the investor receives par, with almost no credit risk.
A retired individual invests $75,000 in a 5-year bank Certificate of Deposit. This investor will be susceptible to:
purchasing power risk and reinvestment risk Purchasing power risk is the risk of inflation. At the CD's maturity, the customer will get back his or her principal, plus interest, but there is no growth in investment value to compensate for inflation. In addition, if interest rates have dropped over the 5 year investment time horizon, when the CD matures, the proceeds would be reinvested at a lower rate - this is a version of reinvestment risk. Unsystematic risk is the risk of an undiversified portfolio. Diversification eliminates this risk. Interest rate risk is the risk that the value of a fixed income security declines in the market as market interest rates rise. This is the same as market risk for a fixed income security. Traditional bank CDs are not traded in the market - the holder can get back his or her principal amount at any time (but there could be an interest penalty). Business risk is the same thing as credit risk for a fixed income security -the risk of default. Bank CDs are covered by FDIC insurance for up to $250,000 per individual, so they are protected against this risk within the dollar limitation. Opportunity cost risk is the risk that another investment of a similar risk profile offers a better return than this one - so the investor has lost the "opportunity" to get a better return with no additional risk taken on. This is a possible risk, but since it is coupled with credit risk as a choice, it cannot be the correct answer.
A customer is considering buying a new $30,000 car and will put $6,000 down and will borrow the remaining $24,000 from the automobile finance company. Assume that this customer has $24,000 in the bank earning 4% interest, but does not wish to use this money to pay for the new car. The loan terms offered are: 12 month loan: 0% 36 month loan: 2% 48 month loan: 6% To determine the cost of the loan, the customer should:
use net present value Net present value analysis can not only be used to assess the best investment choice that gives the best return; it can also be used to assess the least costly financing option (sort of a version of net present cost). This person has $24,000 in the bank earning 4%. The present value of this amount is simply $24,000. Each of the 3 loan options will result in the auto finance payment calculating a monthly payment. If these monthly payments are discounted at 4% (the rate that can be earned "risk-free" by this investor) to today's net present value, the option with the lowest net present value will be the lowest cost choice. Here is a simplified version of the analysis, which discounts the payments on an annual basis instead of a monthly basis. Option 1:12 month loan at 0%$24,000 paid in 1 year1.04= $23,077 NPVTotal NPV = $23,077Option 2:36 month loan at 2%$24,000 paid over 3 years = $8,000 per year.Interest paid at 2% per year = .02 x $12,000 (average balance over life of loan) = $240 per year$8240 paid in 1 year1.04= $7,923 NPV for year 1 payments$8240 paid in 2 years1.04(2)= $7,618 NPV for year 2 payments$8240 paid in 3 years1.04(3)= $7,325 NPV for year 3 paymentsTotal NPV = $7,923 + $7,618 + $7,325 = $22,866Option 3:48 month loan at 6%$24,000 paid over 4 years = $6,000 per year.Interest paid at 6% per year = .06 x $12,000 (average balance over life of loan) = $720 per year$6720 paid in 1 year1.04= $6,462 NPV for year 1 payments$6720 paid in 2 years1.04(2)= $6,213 NPV for year 2 payments$6720 paid in 3 years1.04(3)= $5,974 NPV for year 3 payments$6720 paid in 4 years1.04(4)= $5,744 NPV for year 4 paymentsTotal NPV = $6,462 + $6,213 + $5,974 + $5,744 = $24,393 Thus, Option 1 has a net present cost of $23,077. Option 2 has a net present cost of $22,866. Option 3 has a net present cost of $24,393. Option 2 is the lowest cost option. This long illustration shows how net present value would be used to evaluate the least costly loan or lease. Also note that you do not have to do this for the test! You just have to know the type of situation when it would be used!
