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joja [24]
3 years ago
15

Both Bond Sam and Bond Dave have 7 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has three ye

ars to maturity, whereas Bond Dave has 16 years to maturity. a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam and Bond Dave? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. If rates were to suddenly fall by 2 percent instead, what would be the percentage change in the price of Bond Sam and Bond Dave? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
Business
1 answer:
3241004551 [841]3 years ago
4 0

Solution:

Each bonds have a 7 percent coupon limit. Since sales are also equivalent to 7 percent with par with YTM. The age of Bond Sam is three years and the maturity of Bond Dave is sixteen. At a sudden increase of 2%, interest rates. Decide the shift in both bond price by percentage.

Bond Sam:

Bond Value = pv(rate,nper,pmt,fv)  

Rate = (7%+2%)* 1/2 = 4.5%

nper = 3*2 = 6

fv = 1000

pmt = 7%*1000*1/2 = $35

Bond Value = -pv (4.5%,6,35,1000)

Bond Value =$936.65

Percentage change in the price of Bond Sam = (936.65-1000)/1000 Percentage change in the price of Bond Sam = -6.33%  

Bond Dave:

Bond Value = pv (rate, nper, pmt, fv)

Rate = (7%+2%)*1/2 = 4.5%

nper = 16*2 = 32

fv = 1000

pmt = 7%*1000*1/2 = 35

Bond Value = pv (4.5%,32,35,1000)

Bond Value = $854.66

Percentage change in the price of Bond Dave = (854.66-1000)/1000 Percentage change hi the price of Bond Dave = -14.53%  

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The question is incomplete. Here is the complete question:

The following annual returns for Stock E are projected over the next year for three possible states of the economy. What is the stock’s expected return and standard deviation of returns? E(R) = 8.5% ; σ = 22.70%; mean = $7.50; standard deviation = $2.50

State              Prob     E(R)

Boom             10%     40%

Normal           60%     20%

Recession       30%   - 25%

Answer:

The expected return of the stock E(R) is 8.5%.

The standard deviation of the returns is 22.7%

Explanation:

<u>Expected return</u>

The expected return of the stock can be calculated by multiplying the stock's expected return E(R) in each state of economy by the probability of that state.

The expected return E(R) = (0.4 * 0.1)  +  (0.2 * 0.6)  +  (-0.25 * 0.3)

The expected return E(R) = 0.04 + 0.12 -0.075 = 0.085 or 8.5%

<u>Standard Deviation of returns</u>

The standard deviation is a measure of total risk. It measures the volatility of the stock's expected return. The standard deviation (SD) of a stock's return can be calculated by using the following formula:

SD = √(rA - E(R))² * (pA) + (rB - E(R))² * (pB) + ... + (rN - E(R))² * (pN)

Where,

  • rA, rB to rN is the return under event A, B to N.
  • pA, pB to pN is the probability of these events to occur
  • E(R) is the expected return of the stock

Here, the events are the state of economy.

So, SD = √(0.4 - 0.085)² * (0.1) + (0.2 - 0.085)² * (0.6) + (-0.25 - 0.085)² * (0.3)

SD = 0.22699 or 22.699% rounded off to 22.70%

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