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Assume a bond fund manager manages a portfolio of 50 high yield (speculative) bonds which are mostly rated B. Suppose, based on past experience, the probability of default of one of these bonds in the next year is approximately 11.9%. Suppose the default potential of each bond in this bond portfolio is a binary random variable with mean p and variance p(1-p). Assume default is independent across bonds, so that the number of defaulted bonds in the portfolio will follow a binomial distribution with mean 50p and variance 50p(1-p) where p = 0.119.

(a) Over the next year, what is the expected number of defaults in the portfolio assuming a binomial model for defaults?
(b) Estimate the standard deviation of the number of defaults over the next year.
(c) What is the probability that the number of defaults will be 4 or less over the next year?
(d) Find a 95% confidence interval around the mean for the number of defaults we are likely to see in the coming year (Hint: you may use the following formula: PLEASE SEE JPEG ATTACHMENT).
(e) Critique the use of the binomial distribution in this context.
(f) What would happen to your confidence interval in part (d) if the bond probabilities were not independent of each other?

Let n be the number of bonds (50), p be the probability of each bond defaulting in the next year (0.119), and X be the random variable for the number of bonds defaulting in the next year.

a) Expectation = np = 50(0.119) = 5.95.

b) Standard deviation
= Sqrt(Variance)
= Sqrt(50p(1-p))
= Sqrt(50(0.119)(0.881))
= Sqrt(5.24195)
= 2.29

c) P(X ≤ 4)
= P(X = 0) + ...

Solution Summary

The solution determines statistical calculations for bonds portfolios.

Assume that both X and Y are well-diversified portfolios and the risk free rate is 8%. Portfolio X has an expected return of 14% and a beta 1. Portfolio Y has an expected return of 9,5% and beta 0,25. In this situation, you would conclude that portfolios X and Y________________
a. Are in equilibrium
b. Offer an arbitrage opp

Bonds and stocks are very similar securities in many respects. For example, market value of both are determined by their expected future cash flows; and both show price sensitivity- some more, some less- to a set of common market factors. At the same time, some may even go further and state that when it comes to portfolio invest

Your investment horizon is one year. You observe that the government is offering a completely safe one-year Treasury instrument with a 5 percent return. You also assume that the historical returns above give you the best available information about future expected returns, variances and covariances for the alternative asset cl

What is your interpretation of the efficient frontier and its portfolios? Based on your investment objective what portfolio would you prefer on the efficient frontier and explain why your choice is better than other portfolios with the same or similar objective but are not on the efficient frontier.

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A hypothetical case was set up in which the teller was required to examine a customer's portfolio and determine whether it was more beneficial for the customer to consolidate various CDs into a single issue currently offered, or to leave the portfolio unaltered. A time study made of the teller yielded t

A porfolio consists of the following nine bonds:
1. Reynolds Amern
2. Donnelley RR
3. Altria Group
4. Alcoa Inc
5. Aetna Inc
6. KLA Tencor
7. Hospitality PRO
8. GE Capital
9. Sempra Energy
Part A:
1. For each of the bonds listed above, find the coupon rate, payment date, rating, years to maturity, yields to call,

Bonds and stocks are very similar securities in many respects. For example, market value of both are determined by their expected future cash flows; and both show price sensitivity - some more, some less - to a set of common market factors. At the same time, some may even go further and state that when it comes to portfolio inve

Assume the expected returns, standard deviations, and correlations for well-diversified portfolios of US stocks, US bonds, US real estate and international stocks are given as follows. The risk-free rate is 4%.
Expected Annual Return
Annual Standard Deviation
US Stocks
9%
19%
US Bonds
5.5%
11%
US Real Estate
6%
12%

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Consider the following five problems:
a. Problem 10.31
b. Problem 10.38
c. Problem 10.6
d. Problem 25.4
e. Problem 10.32
Select any three and solve them. In addition to solving these problems, explain the financial impact of the solution or explain how a financial m