Question

(a) Assume that one-year T-bills are currently yielding at 2.8%. It is forecasted that the one-year T-bills in the next few years are 3.1, 2.5%, 3.7%, 4.4% and 5.1% respectively. If the 5-year T-note is yielding at 4.1%, what is its liquidity premium (assuming arithmetic average)?

(b) Before the financial crisis, many corporations have been using CP market as an important funding source to support their daily operations. Explain briefly how this has affected the yield curve based on Market Segmentation Theory.

(c) The 1-year, 2-year, 3-year, 4-year, 5-year, 6-year spot rates are 3.5%, 4.5%, 5.2%, 6.7%, 7.2% and 7.8% respectively. According to Expectations Theory with geometric average, what is the 3-year implied rate at Year 1?

Answer 1

Part (a)

Arithmetic average of the one year T bill rates = (2.8% + 3.1% + 2.5% + 3.7% + 4.4% + 5.1%) / 6 = 3.60%

Hence, the liquidity premium = 4.1% - 3.60% = 0.5%

Part (b)

The CP markets offer securities of very short term maturities. They therefore impact the yield curve for short term maturities. The shape of the CP yield curve (0 to 90 days maturities) is very similar to the yiled curve for short term maturities. Thus based on Market segementation theory:

• Popularity of CP has given way to CP yield curve (usually varying between 0 to 90 days maturity)
• The shpe of this curve impacts the short term yield curve. Thus shape of short term yield curve is similar to CP yield curve.
• CPs don't impact the long term interest rates (as per market segmentation theory)

Part (c)

If r be the the 3-year implied rate at Year 1, then

(1 + s4)4 = (1 + s1)(1 + r)3

Or, (1 + 6.7%)4 = (1 + 3.5%)(1 + r)3

Hence, (1 + r)3 = 1.0674 / 1.035 =  1.2523

hence, the 3-year implied rate at Year 1 = r =  1.25231/3 - 1 = 7.79%