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9/19/2014 CH09 Properties and Pricing of Financial Assets_ Baidu library

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discount rates. Complexity Some assets are complex in that they are actually combinations of two or more assets, eg, a callable bond can be valued as a straight bond plus the value of the put option to the issuer. Even a convertible bond is a putable bond in the sense that the investor has a bond with an option to sell it back to the at a pre-determined price. Tax Status An important feature of any asset is its tax status. Tax rates differ from time to time and country to country. Incomes from bonds are normally taxed, but municipals are free from federal income taxes. Since pension plans are not taxed they do not invest in such bonds.

PRINCIPLES OF PRICING OF FINANCIAL ASSETS The fundamental principle of finance is that the true or correct price of an asset equals the present value of all cash flows that the owner of the asset expects to receive during its life.

PV = CF1 / (1 + r)1 +... + CF N / (1 + r)N where PV = present value of the asset CF = cash flow r = discount rate N = maturity of the financial asset Appropriate Discount Rate The appropriate discount rate, r, Is the return that the market or the consensus of investors requires on the . asset The discount rate can be expressed as:

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. asset The discount rate can be expressed as:

r = RR + IP + DP + MP + LP + EP where RR = real rate of interest IP = inflation premium DP = default risk premium MP = maturity premium LP = liquidity premium

EP = exchange-rate risk premium PRICE VOLATILITY OF FINANCIAL ASSETS A fundamental principle is that a financial asset's price changes in the opposite direction of the change in the required rate of return, or the required yield. It is convenient to measure a change in yield in terms of what market participants refer to as a basis point rather than in terms of a percentage change. Effect of Maturity A change in price is a function of maturity. The longer the period to maturity, the greater is the change in price for a given change in discount rate. Effect of Coupon Rate The lower the coupon, the greater is the of price sensitivity due percentage to the reinvestment factor. While an

increase in interest rates causes a drop in price, it allows interest incomes to be reinvested at higher returns, therefore moderating a price drop. The greatest price sensitivity is associated with zero-coupon bonds, Which

afford no reinvestment of earnings at higher rates. Measuring Price Sensitivity: Duration The duration formula for price sensitivity is as follows:

Price if yield is decreased - price if yield is increased x 100

Initial price x (higher yield - lower yield) The percentage price change for an increase and decrease in interest rates is not the same. Therefore, the average percentage price change per basis point change in yield is calculated as:

P - P + 2 Po ( Δ y) 100

The measure of price sensitivity is called duration. The concept of duration can be interpreted as the number of years for the returns (as reinvested) to equal the initial payout. The higher the number of years, the greater is the duration or price sensitivity. An easy way to apply duration is to see its effect on price changes using the formula:

-D (Change in yield) x 100

We know that if the yield goes up, the price will go down, but by how much? Assume an obtained duration of 9.09 and a -1% increase in yields Then the approximate percentage price change will be.:

-9.09 X .01 x 100 = -9.09% Macaulay duration is a weighted average term-to-maturity of the components of a bond's cash flows, in which the time of receipt of each payment is weighted by the present value of that component. What makes Macaulay duration a valuable measure is that it is related to the price volatility of a bond to changes in yield. The larger the Macaulay duration, the greater is the price sensitivity of a bond to a change in yield.

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Answers to Questions for Chapter 9 (Questions are in bold print followed by answers.)

1. Your broker is recommending that you purchase US government bonds Here is the explanation.: Listen, in these times of uncertainty, with many companies going bankrupt, it makes sense to play it safe and purchase long-term government bonds. They are issued by the US government, so they are risk free. How would you respond to the broker?

US Government bonds may be free of default risk, but they are not free from interest rate risk, which may cause the bond price to decline, resulting in a capital loss should the holder of bond sell it before maturity. Even then there is the inflation premium risk, which means that the principal may have less purchasing power at maturity than it does today. 2. You just inherited 30,000 shares of a company you have never heard of, ABD Corporation. You call your broker to find out if you have finally struck it rich. After several minutes, she comes back on the

telephone and says:. "I do not have a clue about these shares It's too bad they are not traded in a financial market. That would make life a lot easier for you. "What does she mean by this? If the shares are traded on the market, and if the market is efficient, the current price would denote the value of the stock. Without market price information, share value would have to be approximated through other time-consuming and less reliable methods. 3. Suppose you own a bond that pays $ 75 yearly in coupon interest and that is likely to be called in two years (because the firm has already announced that it will redeem the issue early). The call price will be

$ 1,050.What is the price of your bond now, in the market, if the appropriate discount rate for this asset is 9%? PO = $ 75 (PVIFA) 2.09 + $ 1050 (PVIF) 2.09

= $ 75 X 1.7591 + $ 1050 X .8417 = $ 1015.72 4. Your broker has advised you to buy shares of Hungry Boy Fast Foods, which has paid a dividend of

$ 1.00 per year for 10 years and will (according to the broker) continue to do so for many years. The broker believes that the stock, which now has a price of $ 12, will be worth $ 25 per share in five years. You have good reason to think that the discount rate for this firm's stock is 22% per year, because that

rate compensates the buyer for all pertinent risks. Is the stock's present price a good approximation of

its true financial value? PO = $ 1 (PVIFA) 5.22 + $ 25 X (PVIF) 5.22 = .3715 = $ 12.15

The price is right, in fact the stock is slightly undervalued. 5. You have been considering a zero-coupon bond, which pays no interest but will pay a principal of $ 1,000 at the end of five years. The price of the bond is now $ 712.99, and its required rate of return is 7.0%. This morning's news contained a surprising development. The government announced that the rate of inflation appears to be 5.5% instead of the 4% that most people had been expecting. (Suppose most people had thought the real rate of interest was 3%.) What would be the price of the bond, once the

market began to absorb this new information about inflation? The nominal required rate of return is (Real rate plus inflation) ir + if or currently 3% plus 4% = 7 percent. If if becomes 5.5% then the new required rate of return becomes 8.5%. The price of the bond would then be $ 1000 / (1.085)5 or $ 665.05.

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6. State the difference in basis points between each of the following:

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a. 5.5% and 6.5% b. 7% and 9% c. 6.4% and 7.8% d. 9.1% and 11.9%

a. 100 basis points b. 200 basis points c. 140 basis points d. 280 basis points

7.

a. Does a rise of 100 basis points in the discount rate change the price of a 20-year bond as much as it changes the price of a four-year bond, assuming that both bonds have the same coupon rate and offer the same yield?

b. Does a rise of 100 basis points in the discount rate change the price of a 4% coupon bond as much as it changes the price of a 10% coupon bond, assuming that both bonds have the same maturity and offer the same yield?

c. Does a rise of 100 basis points in the discount rate change the price of a 10-year bond to the same extent if the discount rate is 4% as it does if the discount rate is 12%?

a. The price of the 20-year bond will fall more than that of the 4-year bond because there are more years for

the new discount to apply to the cash flows of the 20-year bond. b. The price of the low coupon bond will change more due to the low amount of cash flows that can be

reinvested at the higher rate.

c. A change from the 4% base will lead to a larger change in price. 8. During the early 1980s, interest rates for many long-term bonds were above 14%. In the early 1990s, rates on similar bonds were far lower. What do you think this dramatic decline in market interest rates means for the price volatility of bonds in response to a change in interest rates? Since the direction of the interest rate change is downward, price volatility should increase.

9.

a. What is the cash flow of a 6% coupon bond that pays interest annually, matures in seven years, and has a principal of $ 1,000?

b. Assuming a discount rate of 8%, what is the price of this bond? c. Assuming a discount rate of 8.5%, what is the price of this bond? d. Assuming a discount rate of 7.5%, what is the price of this bond? e. What is the duration of this bond, assuming that the price is the one you calculated in part (b)? f. If the yield changes by 100 basis points, from 8% to 7%, by how much would you approximate

the percentage price change to be using your estimate of duration in part (e)? g. What is the actual percentage price change if the yield changes by 100 basis points?

a. $ 60 a year interest for 7 years plus $ 1000 principal in year 7 for a total of $ 1420 in cash flow. b. 5.2064 X $ 60 + .583 X $ 1000 = $ 895.38 c. 5.119 X $ 60 + .565 X $ 1000 = $ 872.14

d. 5.297 X $ 60 + .603 X $ 1000 = $ 920.82 e. D = $ 920-.82- $ 872.14 = $ 48.68 / 8.95 = 5.44 $ 895.38 (0.85-.075)

f. Applying the formula-D (change in yield) = -5.44 (.01) or a price increase of 5.42%. g. Price at 8% = $ 895.88, at 7% = $ 946.06, so actual percentage change is ($ 946.06 - $ 895.88) / $ 895.88 = 5.6%.

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If the yield changes by 100 basis points, from 8% to 7%, by how much would you approximate

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10. Why is it important to be able to estimate the duration of a bond or bond portfolio? To answer this question, we must understand that duration is related to percentage price change. A simple formula can be used to calculate the approximate duration of a bond or bond portfolio. All we are interested in is the percent price change of a bond when interest rates change by a small amount. To control interest rate risk, it is thus necessary to be able to measure it. Duration provides that measure. 11. Explain why you agree or disagree with the following statement: "Determining the duration of a

financial asset is a simple process. "

Disagree. Determining the duration of a financial asset is not simple process. Because for most assets, the cash flow can change when interest rates change. Therefore, if a change in the cash flow is not considered, duration calculations can be misleading. 12. Explain why the effective duration is a more appropriate measure of a complex financial instrument's price sensitivity to interest rate changes than is modified duration. Modified duration is derived with the assumption that cash flows do not change as interest rates change. Effective duration is calculated with the assumption of changing cash flows. For complex financial instruments' price sensitivity to interest rate changes could be very large. Hence, the importance of effective duration becomes significant.

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