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2024-04-15Calculate the accrued interest of a $1,000, 8% coupon bond.

Assume that the bond's interest payments are made semi-annually and that it has been rated as an investment grade security by the major rating services.

You are currently 45 days into a 182-day coupon period.

$26.73

$9.89

$80.00

$19.78

$14.36

$30.11

$40.00

Since you are currently 45 days into a 182-day coupon period, 24.7% of the interest payment has accrued up until this point. The semi-annual interest payment is $40. Thus .247 × 40 = $9.89.

Accrued interest is the coupon amount earned by the seller between the last coupon date and the settlement date. The buyer must compensate the seller for this amount. In this case, the bond rating was irrelevant to the calculation.

2024-04-14

Assume that you hold a portfolio of bonds as follows:

- $5,000,000 of 5-year bonds with a duration of 3.861 priced at 100 (par)
- $5,000,000 par value of 10-year bonds with a duration of 8.047 priced at 84.6275
- $1,000,000 par value of 30-year bonds with a duration of 9.168 priced at 137.8586

5.5683

7.0253

6.22

2.2375

21.076

6.4847

The duration of the portfolio is simply the weighted average of the components. Each bond segment is first multiplied by its % of value (par, discount, premium) and then multiplied by its duration. Ultimately each segment is divided by the total % of par portfolio value.

In this case, duration = ($5,000,000 × 3.861) / $10,609,961 + ($4,231,375 × 8.047) / $10,609,961 + (1,378,586 × 9.168) / $10,609,961 = 6.22.

2024-04-13

Which of the following is

variance

range of returns

skewness

Sharpe ratio

Sharpe ratio measures the expected returns in excess of the risk-free rate, per unit of risk (measured by the standard deviation). It is not a direct measure of risk, per se. The other three quantities are various measures of risk, variance being the one employed by Markowitz.

2024-04-12

Calculate the current yield for an 8%, 7-year bond whose price is $104.17.

8.50%

7.68%

4.07%

7.00%

3.72%

8.12%

The current yield relates the annual dollar coupon interest to the market price. In this case, current yield = 8 / 104.17 = 7.68%.

The current yield will be greater than the coupon rate when the bond sells at a discount; the reverse is true for a bond selling at a premium. For a bond selling at par, the current yield will be equal to the coupon rate.

2024-04-11

Assume that you hold a callable bond which you wish to analyze. You have noticed during your analysis that the price appreciation of the bond is less than the price depreciation when yields change by 100 basis points (both down and up).

This characteristic is known as ________.

modified duration

negative convexity

positive convexity

non-parallel rate shocks

rate shock

duration

Negative convexity is exhibited by callable bonds if the price decline when yields rise is greater than the price appreciation when yields decrease by the same amount. If the opposite were true, that the price appreciation was greater than the price decline, the bond would be said to exhibit positive convexity.