Reading 6: Discounted Cash Flow Applications-LOS f 习题精选 2011, equivalent, effective, investor, security

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Session 2: Quantitative Methods: Basic Concepts
Reading 6: Discounted Cash Flow Applications

LOS f: Convert among holding period yields, money market yields, effective annual yields, and bond equivalent yields.

 

 

An investor has just purchased a Treasury bill for $99,400. If the security matures in 40 days and has a holding period yield of 0.604%, what is its money market yield?

A) 5.650%.

B) 5.512%.

C) 5.436%.

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The money market yield is the annualized yield on the basis of a 360-day year and does not take into account the effect of compounding. The money market yield = (holding period yield)(360 / number of days until maturity) = (0.604%)(360 / 40) = 5.436%.

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The effective annual yield (EAY) for a T-bill maturing in 150 days is 5.04%. What are the holding period yield (HPY) and money market yield (MMY) respectively?

A) 5.25%; 2.04%.

B) 2.80%; 5.41%.

C) 2.04%; 4.90%.

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The EAY takes the holding period yield and annualizes it based on a 365-day year accounting for compounding. The HPY = (1 + 0.0504)^150/365 = 1.2041 ? 1 = 2.04%. Using the HPY to compute the money market yield = HPY × (360/t) = 0.0204 × (360/150) = 0.04896 = 4.90%.

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A Treasury bill, with 80 days until maturity, has an effective annual yield of 8%. Its holding period yield is closest to:

A) 1.72%.

B) 1.75%.

C) 1.70%.

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The effective annual yield (EAY) is equal to the annualized holding period yield (HPY) based on a 365-day year. EAY = (1 + HPY)^365/t ? 1. HPY = (EAY + 1)^t/365 ? 1 = (1.08)^80/365 ? 1 = 1.70%.

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The holding period yield for a T-Bill maturing in 110 days is 1.90%. What are the equivalent annual yield (EAY) and the money market yield (MMY) respectively?

A) 6.90%; 6.80%.

B) 6.44%; 6.22%.

C) 5.25%; 5.59%.

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The EAY takes the holding period yield and annualizes it based on a 365-day year accounting for compounding. (1 + 0.0190)^365/110 ? 1 = 1.06444 ? 1 = 6.44%. Using the HPY to compute the money market yield = HPY × (360 / t) = 0.0190 × (360 / 110) = 0.06218 = 6.22%.

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If the money market yield is 3.792% on a T-bill with 79 days to maturity, what is the holding period yield?

A) 0.77%.

B) 0.83%.

C) 0.89%.

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The holding period yield can be calculated from the money market yield as: (money market yield) ÷ (360 ÷ t). Therefore, the HPY is (0.03792) × (79 ÷ 360) = 0.0083 = 0.83%.

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A broker calls with a proposal to buy a Treasury bill (T-bill) with 186 days to maturity. He says the effective annual yield on the T-bill is 4.217%. What is the holding period yield if you hold the bill until maturity?

A) 8.44%.

B) 2.13%.

C) 2.02%.

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To calculate the HPY from the EAY, the formula is: (1 + EAY)^(t/365) ? 1. Therefore, the HPY is: (1.04217)^(186/365) ? 1 = 0.0213, or 2.13%.

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If the holding period yield on a Treasury bill (T-bill) with 197 days until maturity is 1.07%, what is the effective annual yield?

A) 0.58%.

B) 1.99%.

C) 1.07%.

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To calculate the EAY from the HPY, the formula is: (1 + HPY)^(365/t) ? 1. Therefore, the EAY is: (1.0107)^(365/197) ? 1 = 0.0199, or 1.99%.

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The effective annual yield for an investment is 10%. What is the yield for this investment on a bond-equivalent basis?

A) 4.88%.

B) 10.00%.

C) 9.76%.

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First, the annual yield must be converted to a semiannual yield. The result is then doubled to obtain the bond-equivalent yield.

Semiannual yield = 1.1^0.5 ? 1 = 0.0488088.
The bond-equivalent yield = 2 × 0.0488088 = 0.097618.

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The holding period yield of a T-bill that has a bank discount yield of 4.70% and a money market yield of 4.86% and matures in 240 days is closest to:

A) 2.8%.

B) 3.2%.

C) 4.9%.

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4.86 × (240/360) = 3.24%.

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What is the effective annual yield of a T-bill that has a money market yield of 5.665% and 255 days to maturity?

A) 5.79%.

B) 5.92%.

C) 4.01%.

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Holding Period Yield = 4.0127% = 5.665% × (255 / 360)

Effective Annual Yield = (1.040127)^365/255 = 1.0571 ? 1 = 5.79%.