1.01.2005

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» Q&A: If the inflation risk is high, how will the central bank...
» Q&A: In the Wall Street Journal, you note that the GNMA yields...
» Q&A: Alan Greenspan, the chairman of the Federal Reserve...
» Q&A: Bootstrap the spot rate for...
» Q&A: Consider an investor with a marginal tax rate of 30%...
» Q&A: Explain the spread between the yield of a TIP strip...
» Q&A: Explain why most of the callable investment-grade corporate bonds...
» Q&A: For bond valuations, what are the two...
» Q&A: Given the prepayment risk of...
» Q&A: Given two identical stock index options...

Q&A: If the inflation risk is high, how will the central bank...

...attempt to contain that risk?

Answer : The central bank will try to tighten the availability of credit, by increasing the target fed funds rate (thus making credit dearer). This will force firms to borrow less, and expand less, leading to lower the pressure on wages. The central bank will try to tighten the availability of credit, by increasing the target fed funds rate (thus making credit dearer). This will force firms to borrow less, and expand less, leading to lower the pressure on wages.

Category: C++ Quant > Finance > Debt

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Q&A: In the Wall Street Journal, you note that the GNMA yields...

...are about 100 basis points higher than Treasuries with comparable maturities. On this basis can we conclude that GNMAs are better investments than Treasuries?

Answer : GNMAs have prepayment risk and the Treasuries do not. As a result, we will expect the GNMAs to trade at a spread over the Treasuries. The 100 basis points should be viewed in this context. It comes down to whether the 100 basis points spread is sufficient to compensate for the prepayment risk.

Category: C++ Quant > Finance > Debt

Your Turn!

 

Q&A: Alan Greenspan, the chairman of the Federal Reserve...

...made the following remark concerning the advantages of introducing TIPS: By routinely monitoring the markets for the indexed and unindexed debt instruments, the Federal Reserve could extract the market's evaluation of the consequences of policy operations. Do you agree with his view? What are the potential problems of inferring inflationary expectations from market prices of TIPS?

Answer : In principle the yields of TIPS and other nominal Treasury securities and Strips may be used to get some information about how the market perceives the future course of real rates and inflation risks.

There are significant measurement problems. Nominal securities tend to be more liquid than TIPS. This liquidity difference is likely to result in significant differences in the yields of these two classes of securities. The yield difference between nominal securities and TIPS also contains inflation risk premium, which may be varying with time. Hence, we cannot interpret the difference between the yield of nominal and indexed securities as strictly a measure of inflationary expectation.

Category: C++ Quant > Finance > Debt

Your Turn!

 

Q&A: Bootstrap the spot rate for...

...the 4th coupon payment period, given the following market data for $100 par Treasury bonds

Period Years Annual YTM (BEY)(%) Price Spot Rate (BEY) (%)
1 .5 3.0   3.0
2 1.0 3.3   3.3
3 1.5 3.5 100 3.5
4 2.0 4.1 100 xxx

Answer

  • 2-year Treasury coupon = 4.1 / 2 = 2.05
  • 1st period cash flow = 2.05 / (1+3/2/100) = 2.02
  • 2st period cash flow = 2.05 / (1+3.3/2/100)^2 = 1.98
  • 3st period cash flow = 2.05 / (1+3.5/2/100) ^3= 1.95
  • 4st period cash flow = (100+2.05) / (1+R/2/100) ^4 = Price - 1st period cash flow - 2st - 3rd = 100 - 2.02 - 1.98 - 1.95 = 94.05. In Excel's rate function, enter FV = 102.055, PV =-94.05, Nper = 4, and one gets R =2%.
  • annualize the spot rate, one should get 4%

Bonus Points

  • The basic principle underlying the bootstrapping method is that the value of a Treasury coupon security should be equal to the value of the package of zero-coupon Treasury securities that duplicates the coupon bond's cash flows.
  • Since the bond is at par the coupon will be the annual YTM multiplied by par.
  • Since spot rates are normally quoted on an annual basis, the calculation needs to adjusted to a semiannual rate.

Category: C++ Quant > Finance > Debt > Valuation

Your Turn!

 

Q&A: Consider an investor with a marginal tax rate of 30%...

...If municipal securities yield 6% and a comparable corporate yields 7.5%, which is the better investment?

Answer : For an investment of $100, the municipal security will provide a yield of $6.00 and the corporate security will provide a yield of $7.50. But given the investor's tax bracket, the after-tax return on the corporate security will be 7.50 * 0.7 = $5.25.

The investor may want to consider other factors, however. Possible tax reforms may cause the tax benefits to be reduced. Plus illiquidity.

Category: C++ Quant > Finance > Debt

Your Turn!

 

Q&A: Explain the spread between the yield of a TIP strip...

...and a nominal Treasury strip with the same maturity.

Answer : Since a nominal strip is more liquid than a TIP strip, it should provide a lower yield. But the nominal strip presents the possibility that it will pay the par amount when the actual inflation risk is a lot higher than what it was expected to be at the time of purchase. This is less of an issue with the TIP security, therefore the TIP strip should provide a lower yield.

Both strips are subject to taxation on accrual. This penalization is more severe for TIP since it is taxed on the inflation accrual as well. The inflation risk premium is also present in TIP due to the lag in the TIP indexing process.

Category: C++ Quant > Finance > Debt

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Q&A: Explain why most of the callable investment-grade corporate bonds...

... are issued during late 1980s and early 1990s.

Answer : Calls were mispriced in the early 1980s but are priced fairly now given the development of options pricing models and other financial innovations in the market that allow the investors to price calls separately from the underlying bond. (The call feature in a perfect market is a matter of indifference: the call gives the issuer the right to call. But the investor will discount the value of the bond by precisely the price of the call option. Callable bonds have a role only if there is a systematic mispricing of the call. Mispricing can be due to two factors. First, the investors tend to undervalue the call relative to the issuers. This will motivate the issuer to issue callable bonds. Second, the issuer is more optimistic than the investors about the future credit reputation. This encourages them to issue callable bonds. If the issuers are right, they can call the bonds when their rating improves. This will enable them to issue cheaper debt later.)

Category: C++ Quant > Finance > Debt

Your Turn!

 

Q&A: For bond valuations, what are the two...

...common apporaches? List some of their key differences.

Answer : The Discounted Cash Flow Valuation approach (DCF) calculates the present value of a financial asset by discounting its expected cash flows at an appropriate interest rate. DCF uses a single interest rate to discount all of a bond's cash flows, regardless of the timing of those cash flows. In reality, each individual cash flow is unique, thereby creating arbitrage opportunities.

The Arbitrage-Free Valuation approach values a bond as a package of cash flows, with each cash flow viewed as a zero-coupon bond and each cash flow discounted at its own unique discount rate. More specifally, V(0) = C/(1 + i(1)) + C/(1 + i(2))^2 + ... + (C + P)/(1 + i(N))^N. It effectively creates a synthetic coupon bond that has the same cash flows as the bond being valued.

Category: C++ Quant > Finance > Debt > Valuation

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Q&A: Given the prepayment risk of...

...a MBS such as GNMA and that of a Z tranche in a CMO, which investors will prefer the Z tranche, which GNMA?

Answer : GNMAs simply pass through the prepayments on a pro-rata basis to the investors. On the other hand, the Z tranche is protected from prepayments for a much longer period because all of the previous tranches have to be prepaid before any prepayments are applied to the Z tranche.

The Z tranche of a CMO will typically have a longer duration than the GNMA and thus should be more attractive to pension funds and insurance companies. GNMAs will be more attractive to investors who have liabilities that are callable because they provide a better asset-liability match.

Category: C++ Quant > Finance > Debt

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Q&A: Given two identical stock index options...

...one offered by exchanges (ie. the listed market) and one by dealers in the OTC market. Are investors indifferent to the choice of these two options?

In the listed markets, the investors get the clearinghouse guarantee. In the dealer markets, they have to rely on the dealer's credit reputation.

It is also much easier to get the options customized in the dealer markets than it is in the listed markets.

Category: C++ Quant > Finance > Derivatives

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