问题如下:
Laura Mathews recently hired Robert Smith, an investment adviser at Shire Gate Advisers, to assist her in investing. Mathews states that her investment time horizon is short, approximately two years or less. Smith gathers information on spot rates for on-the-run annual-coupon government securities and swap spreads, as presented in Exhibit 1. Shire Gate Advisers recently published a report for its clients stating its belief that, based on the weakness in the financial markets, interest rates will remain stable, the yield curve will not change its level or shape for the next two years, and swap spreads will also remain unchanged.
Exhibit 1. Government Spot Rates and Swap Spreads
Smith decides to examine the following three investment options for Mathews:
Investment 1: Buy a government security that would have an annualized return that is nearly risk free. Smith is considering two possible implementations: a two-year investment or a combination of two one-year investments.
Investment 2: Buy a four-year, zero-coupon corporate bond and then sell it after two years. Smith illustrates the returns from this strategy using the swap rate as a proxy for corporate yields.
Investment 3: Buy a lower-quality, two-year corporate bond with a coupon rate of 4.15% and a Z-spread of 65 bps.
When Smith meets with Mathews to present these choices, Mathews tells him that she is somewhat confused by the various spread measures. She is curious to know whether there is one spread measure that could be used as a good indicator of the risk and liquidity of money market securities during the recent past.
3. In presenting Investment 2, Smith should show an annual return closest to:
选项:
A.4.31%.
B.5.42%.
C.6.53%.
解释:
C is correct.
The swap spread is a common way to indicate credit spreads in a market. The four-year swap rate (fixed leg of an interest rate swap) can be used as an indication of the four-year corporate yield. Riding the yield curve by purchasing a four-year zero-coupon bond with a yield of 4.75% {i.e., 4.05% + 0.70%, [P4 = 100/(1 + 0.0475)4 = 83.058]} and then selling it when it becomes a two-year zero-coupon bond with a yield of 3.00% {i.e., 2.70% +0.30%, [P2 = 100/(1 + 0.0300)2 = 94.260]} produces an annual return of 6.53%: (94.260/83.058)0.5 - 1.0 = 0.0653.
老师有一道题有如下的一段解释:
“你说的有一点问题,如果收益率曲线是stable的,我们可以得到future spot rate=current forward rate。换句话说我们站在现在这个时间点看到的forward rate和真的到来将来的时间点的spot rate是一样的,这样才能说明我现在收益率曲线长什么样子,到了将来收益率曲线还是长什么样子,这才是收益率曲线stable的含义。Country C后半句:We assume that future spot rates will be lower than current forward rates for all maturities.这句话就说明收益率曲线不满足yield curve stable的条件了。
而且我们通过表1可以知道,现在C国家的收益率曲线是向下倾斜的,所以你说的“current spot rate 总感觉与riding the curve有点冲突,如果是stable curve,一个4年的债券,两年后的spot rate与current forward rate是一样的话,那么也就代表着现在的S2应该与forward rate(2,2)是一样的啊,因为是stable curve,所以两年后的curve应该与现在的curve完全一样,怎么感觉上面那段话的future spot rate=current forward rate有点不对呢?因为这道题在计算的时候并不使用forward rate来计算的。