Lecture 3 Spot Rates/Forward Rates Flashcards
what is the yield curve?
The yield curve is the graphical depiction of the relationship between the yield on bonds of the same credit quality but different maturities.
Why is the treasury yield curve the one that is most closely watched by market participants?
- The treasury securities are free from default risk and so differences in credit worthiness do not affect yields making these instruments directly comparable
- the treasury market is the largest and most active bond market offering the fewest problems in terms of illiquidity and infrequent trading
What is a spot rate?
The spot rate for a certain maturity is the yield on a zero-coupon treasury of the same maturity
Explain why a financial asset can be viewed as a package of ZCBs
A financial asset generates cash flows over time. The value of the asset is the PV of all the cash flows. Because each cash flow can occur at a different point in time, each cash flow should be valued in today’s dollar using a discount rate that reflects the required rate of return associated with that time period.
How do spot rates related to forward rates?
Forward rates and spot rates are related because forward rates can be derived from spot rates. Forward rates are expected future spot rates that may differ from the actual spot rates that occur in the future.
Respond to: “The yield curve is upward sloping. This suggests that the market consensus is that interest rates are expected to increase in the future
This is not necessarily true because investors demand a greater return as the maturity increases. The maturity premium results from the fact that more uncertainty exists for longer term maturity. Other factors causing the yield curve to be upward sloping include liquidity considerations and supply/demand concerns.
Respond to: “I can’t make sense out of today’s term structure. For short-term yields the spot rates increase with maturity; for maturities greater than three years but less than 8 years, the spot rates decline with maturity; and for maturities >8 years the spot rates are the same for each maturity.
First, there is the pure expectations theory where the forward rates exclusively represent the expected future rates.
Second, there is a liquidity preference theory which asserts that investors do not like uncertainty and so much be offered a higher rate of return for longer maturities. Thus, the forward rate will not only reflect expectations about future interest rates but also a “liquidity” premium that will be higher for longer term securities.
The preferred habit theory also adopts the view that the term structure reflects the expectation of the future path of interest rates as well as risk premium. However, the preferred habit theory rejects the assertion that the risk premium must rise uniformly with maturity. This theory proposes that the shape of the yield curve is determined by both expectations of future interest rates and a risk premium, positive or negative, to induce market participants to shift out their preferred habitat
The market segmentation theory also recognizes that investors have preferred habitats dictated by the nature of their liabilities. This theory also proposes that the major reason for the shape of the yield curve lies in asset-liability management constraints restricting their lending to specific maturity sectors. Thus, the shape shape of the yield curve is determined by the supply and demand for securities within each maturity sector
What treasury issues can be used to construct the theoretical spot rate curve?
A default-free theoretical spot rate curve can be constructed from the yield on treasury securities. The treasury issues that are candidates for inclusion are (i) on the run treasury issues, (ii) on-the-run treasury issues and selected off-the-run treasury issues, (iii) all treasury coupon securities, and bills, (iv) treasury coupon strips
What are the issues with using only the on-the-run treasury issues to construct the theoretical spot rate curve?
First, there is a large gap between some of the maturities points, which may result in misleading yields for those maturity points when estimated using the linear interpolation method.
Second, the yields for the on-the-run issues may be misleading because most offer the favorable financing opportunity in the repo market.
When all treasury issues are used to construct the theoretical spot rate curve, what methodology is used to construct the curve?
The extrapolation method can be used to form the on-the-run or par coupon curve from on-the-run observed yields. This method extrapolates the missing yields from the surrounding maturity points on the par yield curve.
What are the limitations of using treasury strips to construct the theoretical spot rate?
Three problems with using the observed rate on strips:
- the liquidity of the strips market is not as great as that of the treasury coupon market
- The tax treatment of strips is different from that of treasury coupon securities - the accrued interest on strips is taxed even though no cash is received by the investor
- There are maturity sectors in which non-U.S. investors find it advantageous to trade off yield for tax advantages with a strip
What actions force a treasury’s bond price to be valued in the market at the PV of cash flows discounted at the treasury spot rates?
The price of a treasury security should be equal to the PV of its cash flow where each cash flow is discounted at the theoretical spot rates. If this does not occur then an arbitrage situation develops there a large profit can be made with no risk involved. Thus, arbitrage forces a treasury to be priced based on spot rates and not the yield curve. The ability of dealers to purchase securities and create value by stripping forces treasury securities to be priced based on the theoretical spot rates
Explain the role that forward rates play in making investment decisions.
Although a forward rate may never be realized in practice, it is still important for investors because it tells them about their expectations relative to what the market consensus expects. This allows them to make decisions based upon the market expects. For example, forward rates indicate how an investor’s expectations must differ from the market’s consensus in order to make the correct decision
Bart Simpson is considering two alternative investments. The first alternative is to invest in an instrument that matures in two years. The second alternative is to invest in an instrument that matures in one year and at the end of one year, reinvest the proceeds in
a one-year instrument. He believes that one-year interest rates one year from now will be higher than they are today and therefore is leaning in favor of the second alternative. What would you recommend to Bart Simpson?
Bart has two choices. Choice 1 is to buy a 2-year instrument. Choice 2 is to buy a 1YR instrument and then reinvest the value by purchasing another one-year instrument. With choice 1, Bart will realize the 2YR spot rate and that rate is known with certainty. In contrast, with choice 2, the Bart will realize the one-year spot rate, but the one-year rate one year from now is unknown. Bart can make a decision as to what he thinks about future spot rates. For example, suppose Bart expects that one year from now, the one year spot rate will be higher than the forward rate. if so, then Bart will choose choice 2
Price risk
the risk of uncertainty of the bond at the end of the investment horizon. If you do not hold to maturity, price at the time you sell is unknown
