# Compute the number of days in a temporal period.

For consistency, use the difference between calendar dates in Excel when you need to compute the number of days in a temporal period. If any of the coupon dates or other business events fall on a weekend or holiday, ignore this fact and treat them as usual business days.

Problem 1

At some point in 2016, you purchased a 26-week T-Bill maturing on March 2, 2017. On the day of the purchase, the bid for the T-Bill was quoted at 0.473%, following the industry convention for T-Bill quotes.

On the day of the purchase, the bid-ask spread was 0.0022% (see the footnote below) . When the T-Bill matured, you collected the T-Bill’s face value of \$10,000 and realized the holding period return on your investment of 0.1030%.

a) When (on what date) did you make the purchase?

b) What was the yield to maturity on that day? Use the ask price to compute the YTM and state your answer as an APR.

c) What was the effective annualized return (EAR) on your investment?

Problem 2

On May 15, 2014, the Treasury issued a 30-year T-Bond maturing on May 15, 2044. This bond has a par value of \$100 and makes semiannual coupon payments (paid on the 15th of the respective months). The annual coupon rate on this bond is 3.375%.

On January 5, 2015, you purchased 120 of these bonds. You held these bonds for some time, collected the coupons, and sold all the bonds on October 24, 2016. The table below gives the bid-ask spreads (computed as in Footnote 1) and the quotes for the clean ask price of the bond on the purchase and sale dates:

Date Jan. 5, 2015 Oct. 24, 2016

a) What was your total holding period return (in percent) on this investment?

b) What was your effective annualized return?

Problem 3

On June 25, 2016 you purchased a 5-year TIPS security, which has a par value of \$1,000, makes semiannual coupon payments at the annual coupon rate of 2%, and matures on November 30, 2016. The purchase price (dirty price) was \$999.37. You held the security to maturity and the Treasury made all the required payments. At the time when the TIPS security was issued, the reference CPI was 244.0. The table below shows the (hypothetical) CPI values at the end of each month for 2016.

Date CPI value
31-Jan 217.5
28-Feb 218.2
31-Mar 218.8
30-Apr 218.9
31-May 219.4
30-Jun 220.4
31-Jul 223.5
31-Aug 225.5
30-Sep 228.2
31-Oct 229.5
30-Nov 230.1
31-Dec 231.0

a) What was your total holding period return (in percent) on this investment?

b) What was your effective annualized return?

Problem 4

On January 31, 2017, you purchased 2,500 Australian Exchange-traded Treasury Bonds denominated in the Australian dollar (AUD) at 102.50 AUD per bond. In order to make this purchase, you had to exchange your USD into AUD at the rate of 1.3450 AUD per 1 USD. Each of the bonds has a face value of 100 AUD, carries an annual coupon rate of 5.5%, pays coupons semiannually (on the 31st of the respective months), and matures on January 31, 2018. At the time of purchase, the bonds had just paid their semiannual coupon immediately before you purchased them.

You worry about the exchange rate risk and consider two exit scenarios. In both cases, assume that the Australian Treasury will not default on its bonds. Also, when you collect multiple coupons during your holding period (as in scenario (a) below), assume that the coupons are not reinvested and that all coupons collected are kept in AUD until you sell the bonds. At the time of exit (bond sale), all payments obtained from the bonds during the holding period are exchanged into USD in one transaction at the exchange rate prevailing at the time of exit.

You consider two exit scenarios:

a) You will hold the bonds until maturity. What is the break-even exchange rate of AUD to USD (i.e., the maximum number of AUD per USD) on January 31, 2018 such that your total holding period return in USD on this investment is at least not negative? State the exchange rate as AUD per USD.

b) You will collect the July coupon and sell the bonds immediately thereafter on July 31, 2017. Assume that there will be no major interest rate shocks in the Australian market and that the YTM on the bonds will be the same on July 31, 2017 as it was on January 31, 2017. What is the exchange rate (i.e., the maximum number of AUD per USD) at the end of July 2017 such that your effective annualized return in USD on this investment is at least 2%? State the exchange rate as AUD per USD.

Problem 5

The Treasury issued a 2-year T-Note, a 3-year T-Note, and a 5-year T-Note on the same day. All these notes have a par value of \$100 and an annual coupon rate of 1.20%. Their prices on the day of the issue were \$99.4111, \$99.1232, and \$98.5602, respectively. As usual, the coupons are paid semiannually. You purchased a 3-year T-Note and a 5-year T-Note on the day they were issued.

a) What do the prices of the notes at issue tell you about the shape of the yield curve? (Use the YTMs of the T-notes as proxies for the respective spot rates)

b) Fast-forward two years (the notes you hold have just paid their fourth semiannual coupon). The yield curve has shifted up by 100 basis points across all the maturities of Treasuries. You decide to sell both the 3-year note and the 5-year note immediately after collecting their coupons. What are your effective annualized returns on the 3-year note and on the 5-year note?

c) Consider the YTMs from part (a) and now express them as an EAR (effective annualized return), which measures the expected annual return on investing in the notes. Compare these effective annualized returns at purchase and the actual effective annualized returns you earned in part (b) for the 3-year and 5-year notes. Explain why the gap between the expected and the realized return is so different between the 3-year and the 5-year notes, despite the fact that both bonds were affected by the shift in the yield curve of equal magnitude (100 bps).