CH09 Properties and Pricing of Financial Assets_ Baidu Library

9/19/2014

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The Th e firs firstt teac teach h carnival ... topic CH01 Introduc CH02 Financial CH03 CH 03 De Depo posi sito to CH11 The Term CH13 Primary

CH09 Properties and Pricing of Financial Assets No evaluation

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CH09 Properties and Pricing of Financial Assets_ Baidu library

discount rates.

Some assets are 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 in the sense that the investor has a bond with an option to sell it back to the at a pre-determined price.

An important feature of any asset is its . 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.

The fundamental principle of finance is that the true or correct price of an asset equals the cash flows that the owner of the asset expects to receive during its life. PV = CF1 / (1 + r)1 +... + CF where

PV =

present value of the asset

CF = r= N =

cash flow discount rate maturity of the financial asset

N /

of all

(1 + N r)

The appropriate , r , Is the return that the mar ket or the consensus of investors requires on the . asset The discount rate can be expressed as: http://wendang.baidu.com/view/f6b87342f46527d3240ce089.html

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r = RR + IP + DP + MP + LP + EP where RR = IP = DP = MP = LP = EP = 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 . It is convenient to measure a change in yield in terms of what market participants refer to as a rather than in terms of a percentage change.

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.

The lower the coupon, the greater is the of price sensitivity due percentage to the r einvestment factor. While an increase interest rates causes a drop in price,price it allows interest towith be reinvested at higher returns, thereforein moderating a price drop. The greatest sensitivity is incomes associated , Which

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afford no reinvestment of earnings at higher rates.

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 (C hange 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%

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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(

are in bold print followed by answers.)

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.

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and says:. do not make have alife clue about these It s toodoes badshe they are not traded in a financial market. ThatI would a lot easier forshares you. What 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 timeconsuming and less reliable methods.

PO = =

$ 75 (PVIFA)2.09 + $ 1050 (PVIF) 2.09 $ 75 X 1.7591 + $ 1050 X .8417 = $ 1015.72

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You have good reason to think that the discount rate for this firm s stock is 22% per year, because that s the buyer for all pertinent risks. Is the stock s present price a good approximation of '

PO =

$ 1 (PVIFA)5.22 + $ 25 X (PVIF) 5.22 = .3715 = $ 12.15

The price is right, in fact the stock is slightly undervalued.

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7.0%. This morning s news contained a surprising development. The

The nominal required rate of return is (Real rate plus inflation) i r + 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 5 $ 1000 / (1.085) or $ 665.05. http://wendang.baidu.com/view/f6b87342f46527d3240ce089.html

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a. b. c. d.

a. b. c.

100 200 140 280

basis basis basis basis

points points points points

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. 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. A change from the 4% base will lead to a larger change in price.

CH09 Properties and Pricing of Financial Assets

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Since the direction of the interest rate change is downward, price volatility should increase.

O N

c N

c N

In N

M N

a. b. c.

$ 60 a year interest for 7 years plus $ 1000 principal in year 7 for a total of $ 1420 in cash flow. Original text 5.2064 X $ 60 + .583 X $ 1000 = $ 895.38 If the yield changes by 100 basis points, from 8% to 7%, by how much would you approximate If you 5.119 X $ 60 + .565 X $ 1000 = $ 872.14 pleas

d. e.

5.297 $ 60 + $.603 X $ 1000 = $ 920.82 D=$X 920-.82872.14 = $ 48.68 / 8.95 = 5.44 $ 895.38 (0.85-.075) Applying the formula-D (change in yield) = -5.44 (.01) or a price increase of 5.42%. Price at 8% = $ 895.88, at 7% = $ 946.06, so actual percentage change is ($ 946.06 - $ 895.88) / $ 895.88 = 5.6%.

f. g.

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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 ar e 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. 5 / 6

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Explain why you agree or disagree with the following statement: Determining the duration of a inancial asset is a simple process.

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Disagree. Determining the duration a financial asset isifnot simpleinprocess. assets, duration the cash flow can change when interest rates of change. Therefore, a change the cashBecause f low is for not most considered, calculations can be misleading.

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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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