Questions and answers
Prepare calculations and a one-two-page analysis (excluding the title and references pages) that addresses the following questions:
Assuming that the expectation theory is the correct theory of the term structure, calculate the interest rates in the term structure for maturity. Next, plot the resulting yield curves for the following series of one-year interest rates over the next five years using both a and b.
The expectations theory associated with the term structure asserts that the rate of interest for a long-term bond will be the same to a mean of the short-term interest rates that is expected to transpire over the existence of the long-term bond (Mishkin et al, 1998).
5%, 7%, 7%, 7%, 7%
Interest rate for a 1-yr bond = i11= 5%1=5% interest rate on a 2-yr bond = i1+i1e2= 5%+7%2=6%
Interest rate on a 3-yr bond = i1+ i1e+ i2e3= 5%+7%+7%3≈6.3%
4-yr bond = i1+ i1e+ i2e+ i3e4= 5%+7%+7%+7%4≈6.5%
5-yr bond interest rate = i1+ i1e+ i2e+ i3e+ i4e5= 5%+7%+7%+7%+7%5≈6.6%
The term structure for:
b) 5%, 4%, 4%, 4%, 4%
1-yr bond interest rate = i11= 5%1=5% 2-yr bond interest rate = i1+i1e2= 5%+4%2=4.5%
3-yr bond interest rate = i1+ i1e+ i2e3= 5%+4%+4%3≈4.3%
4-yr bond interest rate = i1+ i1e+ i2e+ i3e4= 5%+4%+4%+4%4≈4.25%
5 yr bond interest rate =i1+ i1e+ i2e+ i3e+ i4e5= 5%+4%+4%+4%+4%5≈4.2%
Resulting yield curves:
For a)
For b)
Discuss how your yield curves would change if people preferred short term bonds over long term bonds.
If people preferred shorter-term bond to longer-term bonds, for (i) the yield curve that is upward-sloping would become more steeper since there would be a positive liquidity premium for long-term bonds. This liquidity premium is required to be added to 2-year upto 5-year bonds interest rates hence leading to steeper upward sloping. For (ii), the steep would be less and at times may end up with a minor positive upward slope especially if it is a case of positive risk premium for the long-term bonds. In which case, it comes out that the nature of the yield curve is dependent on the extent liquidity premium (Mishkin, 1994).
Explain what the textbooks suggests will happen if the short term rate is much cheaper than the long-term interest rate.
In a case where the short-term rate is much cheaper, the rate of investment will reduce. This is because the long-term interest rate is much higher thereby barring people from investing and other kinds of spending. The investors will be much triggered to go for the cheaper short-term rate. The government normally makes the long-term interest rates cheaper in a case where they would want to trigger much investment.
Explain whether or not that is a normal occurrence or a cause for alarm
This is a normal condition since it gives an upward rising slope. In which case, the upward slope is a reflection of the normal scenario showing that short term will be lesser in terms of interest rate as compared to long-term interest rate. This can be explained in terms of the higher risks associated with long term securities which makes them have a higher return (Mishkin, 1994).
References
Mishkin, F. S., Eakins, S. G., & Mishkin, F. S. (1998). Financial markets and institutions. Reading, Mass: Addison-Wesley.
Mishkin, F. S. (1994). Financial markets, institutions, and money. New York, N.Y: HarperCollins College Publishers.
