Question:

Firm A issues a zero-coupon bond with a face value of $100,000 at

the beginning of the first year (t=0) which is purchased by investor B. The

bond matures at the end of 20 years (t=20). The prevailing interest rate at

t=0 for bonds with similar risk is 5%.

Consider the following for Investor B:

(a) How much does Investor B pay for this 20-year $100,000 zero-coupon bond

at t=0? What is the yield to maturity?

(b) Suppose that when markets open on the first day of the sixth year, the

interest rate is still 5%. What would be the price of the bond that

morning?

(c) Suppose that by the time the markets close on the first day of the sixth

year, interest rates have fallen to 4%. What would be the price of

Investor B's bond at the end of the day? (For calculations, ignore the

fact that one day has passed, just assume we are still at the beginning

of the sixth year).

(d) Suppose Investor C buys Investor B's bond at the beginning of the ninth

year for $60,000. Assuming this was a fair exchange, what does this tell

you about the movement of interest rates between the beginning of the

sixth year and the beginning of the ninth year?

(e) Redo (b) and (c) in the case that the bond that Firm A issued at

t=0 was

actually a 30-year bond rather than a 20-year bond. What does your answer

tell you about the relationship between time to maturity and price

volatility?

Problem 2:

Prove mathematically that for a level coupon bond, the discount

rate equals to the coupon rate, if the bond price is the face value

29. Comprehensive, correlation analysis is performed weekly on a biomedical x, y data set with a large sample size of N > 2c6 that increases weekly by Al input of data from on-line medical records and from sensor feeds of wearable devices, e.g., implants, smart watches, Pearson r remains significant, as performed weekly, yet the magnitude of Pearson r fluctuates greatly. And, graphical visualization of scatter plots is frustrating due to over-plotting of points which makes dense "ink" blobs across the graphs. The analysts decide to apply a lowess fit each week to the ever growing scatter plots. Statistically, why the lowess fit? 3, as EDA b. to detect nonlinear trends C. to guide the eye d. to detect clusters e. to detect x, y "features" f. to assess linearity g. to explore the x, y data h. all the above 30. Consider this code chunk entered at the R Console. The LAST LINE of R code below, returns 3 rl 12 plot (rl, r2) I scatter plot cor. test (rl, r2, conf. level=. 99) a. Pearson r with two-sided significance test and 99% Cl of r b. Pearson r with two-sided significance test and 95% Cl of r c. Spearman r with one-sided significance test d. Pearson r with one-sided significance test and 99% Cl of r e. Spearman r with two-sided significance test f. Pearson r with one-sided significance test and 95% Cl of r 4- none of the above 31. The x, y data encoded in R below, is suitable for correlation analysis. Which of the following is both statistically accurate and written in the best format for reporting in a research paper. > x