Financial engineering principles phần 9 docx

To provide an example outside of the broader strokes of product types, con- sider the effect of different prepayment speeds on the outstanding balance of principal for an MBS. Figure 5.36 embodies a set of scenarios to be considered. As shown, prepayment speeds can have a very important impact indeed on the valuation of an MBS, and these speeds can vary from month to month. Just as these types of illustrations can be useful with evaluating the risk of a particular security, they also can be used to evaluate the risk pro- file of entire portfolios. Another popular way to conceptualize the risks of a portfolio is with scenario analysis. “Scenario analysis” refers to evaluating a particular strategy and/or port- folio construction by running it through all of its paces, all the while taking Risk Management 233 0 0 Price (Exchange rate) Passage of time Purchase price Soft floor for currency value (Embedded credit call) Currency FIGURE 5.35 Price cone for currencies. TABLE 5.7 Comparison of Total Return Components for a One-Year Horizon Products Bonds Equities Currencies Cash flow End price Yes No No Cash flows Yes Yes N/A Reinvestment of cash flows No No N/A 05_200306_CH05/Beaumont 8/15/03 12:52 PM Page 233 note of how total return evolves. For example, for a proposed bond port- folio construction, a portfolio manager might be interested in observing how total returns look on a six-month horizon if the yield curve stays relatively unchanged, if the yield curve flattens, or if the yield curve inverts. The total returns for these different scenarios then can be compared to the prevailing six-month forward yield curves and to the portfolio manager’s own personal forecast (should she have one), and the proposed portfolio construction then can be evaluated accordingly. A variety of instrument types can be layered onto this core portfolio, including futures and options, so as to incorporate the latter. Additional scenarios (or “stress tests” as they are sometimes called) also might be performed that include different assumptions for volatility. Scenario analysis can help give investors a working idea of the risks and rewards embedded in a particular strategy or portfolio structure before the plan is actually put into place. Of course, regardless of the number of what- if scenarios applied, the actual experience may or may not correspond exactly to any one of the scenarios. In this regard the value of scenario analysis lies in helping to identify boundary conditions. In a more macro context of risk, consider the challenge of linking envi- ronmental dynamics with financial products. Let us assume that a company 234 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT 0 5 10 15 20 25 30 0% PSA 50% PSA 120% PSA 200% PSA Remaining balance (%) Passage of time FIGURE 5.36 Outstanding principal balances for a generic “current coupon” 30-year pass-thru. 05_200306_CH05/Beaumont 8/15/03 12:52 PM Page 234 is headquartered in country X with a rather large and important subsidiary in country Y. Further, assume that the currencies in country X and Y are dif- ferent and that the company repatriates its profits on an annual basis to its home base. It would be rather straightforward to envision a scenario whereby the subsidiary in country Y has a very profitable year but where those profits would quickly diminish after the relevant exchange rate were applied. This reflects a situation where the currency of country Y depreci- ated in a significant way relative to the currency of country X. If the company had elected at the start of the year to hedge its currency exposures on an ongoing basis when and where practical, likely its profitability would have been at least partially protected. Accordingly, this strategy is often called an economic hedge. The motivation for the strategy would be to protect against a macro-oriented business level exposure (as opposed to a more micro-oriented portfolio- or product-level exposure). Other examples include an energy-sensitive industry, such as an airline, using oil futures to hedge or otherwise protect against high fuel costs, or a rate-sensitive indus- try, as with banking, using interest rate futures to hedge or protect against adverse moves in rates. Summary Probability plays a central role in attempts to characterize an investment’s total return. In the absence of uncertainties, probability is 100 percent. As layers of risks are added, a 100 percent probability is whittled down to some- thing other than complete certainty. In the classic finance context of a trade- off between risk and reward, riskier investments will generate higher returns over a long run relative to less risky investments, assuming there is some diversification within respective portfolios. As another perspective on the inter-relationship between probability and products, consider Figure 5.37. With probability on one axis and time on the other, it shows profiles of a sample bond, equity, and currency. As shown, a product’s price is known with 100 percent certainty at the time it is purchased, and there is a relatively high degree of certainty that its price will not change dramatically within a short time after purchase. However, as time from purchase date marches onward, the certainty of what the price may do steadily declines. However, in the case of bonds, which have known prices at maturity, the pull to par eventually becomes a dominant factor and the probability related to price begins to increase (and reaches 100 percent at maturity for a Treasury security). The lower equity and cur- rency profiles are consistent with the higher uncertainty (lower probability) associated with these products relative to bonds. (The standard deviation of price tends to be lowest for bonds, higher for equities, and higher again for currencies.) Risk Management 235 05_200306_CH05/Beaumont 8/15/03 12:52 PM Page 235 CHAPTER SUMMARY As we have seen time and again, we do not need to venture very far in the world of finance and investments to come face-to-face with a variety of risk consid- erations. If all we care about is a safe investment with a six-month horizon, then we can certainly go out and buy a six-month Treasury bill. There is no credit risk, reinvestment risk, or price risk (as long as we hold the Treasury bill to maturity). But what if we have a 12-month horizon? Do we then buy a 12- month Treasury bill, or do we consider the purchase of two consecutive six- month bills? What do we think of the price risk of a six-month Treasury bill in six months? In sum, there is risk embedded in many of the most fundamental of investment decisions, even if these risks are not explicitly recognized as such. When investors purchase a 12-month Treasury bill, they are implicitly (if not explicitly) stating a preference over the purchase of: a. Two consecutive six-month Treasury bills b. Four consecutive three-month Treasury bills c. Two consecutive three-month Treasury bills, followed by the purchase of a six-month Treasury bill d. A six-month Treasury bill, followed by the purchase of two consecutive three-month Treasury bills, or e. A three-month Treasury bill, followed by the purchase of a six-month Treasury bill, followed by the purchase of another three-month Treasury bill 236 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT Time 100% Bond Equity Currency Maturity of the bond 0 0 Probability FIGURE 5.37 Probability profiles of a sample bond, equity, and currency. 05_200306_CH05/Beaumont 8/15/03 12:52 PM Page 236 Although the risks among these various scenarios may be minimal with Treasury bills, the point here is to highlight how the decision to pursue strat- egy option a necessarily means not pursuing strategy b (or c or d, etc.). There are consequences for every investment decision that is taken as well as for each one that is deferred. In addition to the various risk classifications presented in this chapter, there is also something called as event risk. Simply put, event risk may be thought of as any sudden unanticipated shock to the marketplace. It is not prudent for most portfolio managers to structure their entire portfolio around an event that may or may not occur. However, it can be instructive for portfolio managers to know what their total return profiles might look like in the event of a market shock. Scenario analysis can assist with this. Further, it also may be instructive for portfolio managers to know how prod- ucts have behaved historically when subject to shocks. One way to concep- tualize this would be with a charting of relevant variables as in Figure 5.38. In sum, risk is elusive; that is why it is called risk. Simply dismissing it is irresponsible. By thinking of creative ways in which to better understand, classify, and manage risk, investors will be better equipped to handle the vagaries of risk when they arise. Risk Management 237 Event risk (Grouped by standard deviation [SD]) Credit risk Total return AA A AAA 1 to 3 0 3 to 6 6 to 9 The intersection of low event risk (0–3 standard deviations of price risk), double- A credit risk, and a slightly positive total return ϩ Ϫ FIGURE 5.38 Another conceptual mapping of risk profiles. 05_200306_CH05/Beaumont 8/15/03 12:52 PM Page 237 APPENDIX Benchmark Risk At first pass, having the words “benchmark” and “risk” together may seem incongruous. After all, isn’t the role of a benchmark to provide some kind of a neutral measure, some kind of pure yardstick by which to gauge rela- tive market performance? While that certainly is the ideal role of a bench- mark, with the dynamic nature of the marketplace generally, it often is an ideal that is difficult to live up to. For example, for decades U.S. Treasuries were seen as the appropriate benchmark for divining relative value among bonds. In the late 1990s, with the advent of unexpected and persistent federal budget surpluses, this sta- tus began to look a little shaky. With Treasuries on a relative decline, investors began to ask if there might be another benchmark security type that could replace Treasuries as an arbiter of value. A particular financial instrument does not become a benchmark by formal decree; it is much more by what the market deems to be of relevance in a very practical way. That is, the marketplace naturally gravitates toward obvious solutions that work rather than pursue solutions that may be more theoretically pure though less practical. Indeed, during the 1970s in the United States, longer-dated cor- porate securities were used as market benchmarks, largely because they were more prevalent at that time than the burgeoning federal budget deficits that dominated the 1980s. In the late 1990s and into 2000, a debate was waged as to whether federal agency debt might represent a more appropriate mar- ket benchmark in light of the agencies’ net growth of issuance contrasting against a net contraction in Treasuries. Indeed, the likes of Fannie Mae and Freddie Mac introduced a regular cycle to key maturities in their debt man- agement program to provide a market alternative to Treasuries. Over the period of debate the federal agencies were greatly increasing their borrow- ing programs relative to the U.S. government. Another vehicle that sometimes is named as a benchmark possibility is the swap yield. Proponents of this variable do not hold it up as a paragon of market solutions, since it (like any one single variable that would be selected) has its own strengths and weaknesses. As benchmark candidates, swap yields have these points going for them (listed in no particular order). Ⅲ Swap yields have a tried-and-true history of assisting with relative value identification in European markets. Ⅲ Many markets around the globe (and notably within Asia) have for a long time run federal budgets that have at least been neutral if not in surplus, 238 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT 05_200306_CH05/Beaumont 8/15/03 12:52 PM Page 238 and in the absence of being able to defer to swap yields would have no other benchmark candidates in common with other markets globally. Ⅲ As is perhaps now obvious in light of the two preceding points, if swap yields were adopted in the U.S. market as a benchmark prototype, they could easily translate into every market around the world. Ⅲ Considering the possibility (at least as of this writing) of the U.S. fed- eral government cutting its ties to federal agencies by no longer agree- ing to back their debt implicitly, with the stroke of a pen the agencies could very well become much more like non-Treasury instruments than Treasury instruments. In this regard, if agencies were to become much more creditlike anyway, then why not just revert to swap yields? This question and others serve to highlight how the fluidity of the market- place often affects the role and value of market benchmarks, and investors are well advised to stay abreast of benchmark-related topics, especially if the portfolio performance of interest to them is a perfor- mance relative to a benchmark measure. As pointed out in the appendix to Chapter 4, a benchmark may best be thought of as a moving target rather than a static one. While this is obvi- ous in the context of fast-moving markets, in some instances it can be just as important when nothing really happens, as with fixed income securities. While it may seem obvious to say that the value of a fixed income instru- ment is going to be influenced by changes in interest rates, a variety of things can impact the nature of those changes. Clearly, if a 10-year-maturity Fannie Mae bullet is being quoted relative to the yield of the 10-year Treasury, then the rise and fall in yield of the Treasury presumably will translate into the rise and fall of the yield on the Fannie Mae issue. However, if a new 10-year Treasury happens to come to market (as of this writing, a 10-year Treasury comes to market every quarter) and becomes the new issue against which the Fannie Mae security is quoted, then the yield spread of the Fannie Mae relative to the Treasury may change. Its change would not be attributable to anything new or different with Fannie Mae as a credit risk, nor, for that matter, to anything new or different with the Treasury as a credit risk, but solely because a benchmark Treasury rate has “rolled” into a new bench- mark rate. Another type of interest rate risk, and clearly a broader definition of the “roll risk” just described, is “roll-down” risk. “Roll down” is a term used to describe the fact that the yield curve typically has a slope to it, and as time passes, a 10-year security is going to roll down into a 9-year maturity, then an 8-year maturity, and so on. This phenomenon is called “roll down” because the typical shape of the yield curve slopes upward, with yields at shorter maturities being lower than yields for longer maturities. Thus, rolling down the yield curve into shorter maturities generally would mean Risk Management 239 05_200306_CH05/Beaumont 8/15/03 12:52 PM Page 239 rolling down into lower yield levels. However, this may not always be the case. Indeed, even if the overall curve tends to have a normal upward slope to it, there may be special cases where there is “roll-up.” For example, if a widely anticipated newly issued Treasury were to come to market and with strong demand, it may very well find itself “on special” and trading with a lower yield, even though it has a maturity that is slightly longer than the shorter-maturity Treasury that it is replacing. In sum, benchmarks can be misleading if thought of only as static and unchanging arbiters of relative value. They are fluid and dynamic, and if they are indeed the enemy to be beaten for a value-oriented investor, then taking the time to understand and appreciate the nature of a particular index would be time well spent indeed. 240 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT 05_200306_CH05/Beaumont 8/15/03 12:52 PM Page 240 Market Environment 241 CHAPTER 6 Legal & regulatory Investors Tax Tax This chapter continues with a more macro orientation toward investments, examining tax, legal and regulatory, and investor-related issues. Specific cases of how products and cash flows are affected by these macro dynamics, and more general cases of how investment decision making is affected are presented. Although perhaps all to easy to dispense with in the excitement of invest- ing, paying taxes is, regrettably, a fact of life — unless one is investing on behalf of not-for-profit entities. Taxes can make a very large impact on an investor’s realized total returns. The goal of this chapter is to highlight how consideration of taxes can have a very important impact on an investor’s decision making. In the United States, as in most other developed financial markets, equi- ties and bonds can be subject to a variety of different tax structures. There is the capital gains tax, which is differentiated into a short-term rate (for holding periods of less than one year) and a long-term rate (for holding peri- ods of more than one year). As an incentive to investors to hold on to their 06_200306_CH06/Beaumont 8/15/03 12:54 PM Page 241 . (3) Fannie Mae 2 5.66 4.47 3 .91 3.34 FHLB 21 5.66 4.81 4.25 3.68 Single-A corporate bond 59 6.04 4.77 4.17 3.56 10-year Maturities Fannie Mae 30.5 5. 89 4.65 4.06 3.47 FHLB 30.5 5. 89 5.00 4.41 3.83 Single-A. prevalent at that time than the burgeoning federal budget deficits that dominated the 198 0s. In the late 199 0s and into 2000, a debate was waged as to whether federal agency debt might represent. consider the challenge of linking envi- ronmental dynamics with financial products. Let us assume that a company 234 FINANCIAL ENGINEERING, RISK MANAGEMENT, AND MARKET ENVIRONMENT 0 5 10 15 20