Financial Engineering

陳明道 教授David M. Chen (dmc)

003924@mail.fju.edu.twwww.tej.com.tw/effas

Mason, Scott P., Robert C. Merton, Andre F. Perold, and Peter Tufano, Prentice-Hall Inc., 1995.

ContentFinancial systemFinancial innovationFinancial engineeringBenefit of financial innovationSocial valueInternational dynamicsSecurities innovationFuture implicationsThe structure of interest rateDuration and convexity

Financial SystemFunctional perspective

Allocation and deployment of resources in an uncertain environmentAcross time and spatially

Basic cash-flow cycle: household savings to investments by firms to investment returns for consumption and new savings.

Payment systemPooling of funds

Risk-pooling and risk-sharing opportunities: bigger firms or projects, mutual funds

Manage uncertainty and control risk

Price discoveryKey source of information for coordinating decentralized decision-making

Deal with information asymmetry* Through capital markets composed of

MoneyFixed-incomeEquityDerivatives

Served by financial intermediationThe process of transforming financial assets from one form into

anotherUnderwriting & synthesizing: input/output production

Financial InnovationAreas

Creation of new types of securitiesWhile options and futures may not be entirely new,

the proliferation of organized trading market in both equity and fixed-income derivative securities during the past two decades is unprecedented.

Development of standardized markets was absolutely essential for the subsequent creation of a wide range of financial products.

Development and evolution of new financial organizations (and processes)

Changes in institutional structure evolve toward improvements in the performance of the functions of the financial system.

Institutional perspective hinders economic efficiency (institution preservation)*

The functional perspective views financial innovation as the engine driving the financial system toward its goal of economic efficiency. Even national governments are increasingly acting more like competitive institutions in this domain.

Means for implementing innovationThe process of tailoring financial instruments and

organizational structure to improve the profitability of customersSteps

Diagnosis: nature and source of the problemAnalysis: finding the best solutionDesign: new instruments or intermediaryProduction: underwriting or synthesizing or bothPricing: cost and profit marginCustomization: tailoring to the specific needs.Standardization: organized exchange

Financial engineering

Embodies the skills, techniques, and processes of innovation

Technologies Pricing and hedging concept

Support more comprehensive derivative-securities markets and risk-management systems.

Computer speed and capacityEnable systems to securitizes assets and monitor thousands of

trading positions in real time.Communication systems

Facilitate simultaneous actions needed to exploit transient arbitrage opportunities.

Risk ManagementSelling the source

Hedging: moving from risky to risklessFutures, forward contracts, and swaps

Diversification Basket cash-market securities and index futures

Buying insuranceRetention of the upside while deleting downsideOptions (on aggregate portfolios)

Example: Insured-equity productEquivalent to a protective-put option strategy: buying

the stock or index and its put optionChase Manhattan Bank: market-index (S&P 500)

certificate of depositSwiss Bank: guarantee-return-on-investment securities

(GROIS)• Not appropriately named, does not guarantee ROI but

principalMerrill Lynch: market index target term securities

(MITTS)LOR: supertrust and supershares

UnderwritingCreating a unit trust: buying the stock or index (ETF) and

treasury bills with a face value equal to the guaranteed amount

Serving as an agent of the trust by issuing two classes of securities: Class A the insured-equity product with payoff = max (stock price, TB) and Class Z the residual = min (stock price, TB)

Class Z happens to have the same structure as a junk bond.Otherwise, Class Z must be regarded as cram-downs 填塞

reflecting the lack of natural investor demand for its pattern of payoffs, and must be sold on discount to bargain hunters.

SynthesizingAs principle owner (not agent of the trust)Finance the difference between the cost of two assets and the proceeds

from sale of the insured-equity product with equity capital.Potentially significant agency and tax (dead weight 淨負荷 ) costs of

equity capital of firms. Owner of the stock may have an incentive to sell Class A with a

higher price and retain Class Z.Synthesizing or dynamic-trading to replicate the payoff structure in the

least-cost way with an initial investment without further infusion of capital (self-financing, riskless arbitrage)

Assembling customer-tailored products with a single (static) replication of the aggregate payoff.

Clerical error, model misspecification, credit risk of the intermediary.

Benefits of InnovationEfficient resource allocation

Lowering transaction costsCompleting marketsMaking prices more informative

Form of benefitsLowering costs of raising fundsManaging risk exposures more preciselyEnhancing investment returnsCoping with changing tax and regulatory regimes

Social ValuePerformance appraisal

Effectiveness of the financial systemImproved opportunities for households to receive

efficient risk-return tradeoffs and more effective tailoring to individual needs over the entire life cycle.

Expanded economic or managerial flexibilitySolving long-standing and vexing problems of

corporate finance, financial services, investment management, and public policy.

NegativeEx ante distortions of capital allocation

Unrealistic expectations of greater expected returns with less risk fueled by financial-services firms and organized exchanges that see huge profits from the vast activity .

Ex post excessive volatility in capital market pricesFaulty expectations not realized.

PositiveDevelopment of a national mortgage market in the 1980s

along with a wide range of MBSTransformed residential housing finance from fragmented, local-

based sources to a free-flowing, international base of capital.

Derivative markets Made it possible for business firms to hedge effectively against

financial risks.Mutual funds

Directly benefit households around the world.Should be evaluated within the context of the managerial or

public-policy decisions to which it is applied.

Example: international stock-returns swapsDiagnosis & Analysis

International diversification has not yet evolved in many smaller, developed countries.

• Capital controls to prevent flight of domestic capital and to reduce the risk of inadequate domestic investment.

High transaction cost offsets any diversification benefitsDomestic physical investment is driven to become more diversified than

necessary• International diversification is more efficient than domestic

diversification.Proposed solution

Separating the capital flow effects of investment from the risk-sharing aspects.

DesignSwap

The total return per dollar on the small country’s domestic stock market is exchanged annually for the total return per dollar on a market-value weighted-average of the major world stock markets.

Through domestic mutual funds or financial intermediariesForeign investors benefit by avoiding the costs of trading in

individual securities in the local markets and by avoiding some tax complications.

Exchange of returns could be in a common currency or adjusted to different currencies with currency-swap agreements.

In notional or principal amount of the swap.No initial payment by either party. Settlement involves only the difference between the total returns

on the two stock market indices. The small-country investors make net payments out precisely when their local market has outperformed the world markets.

Trading and ownership of actual shares remain with domestic investors.

Institutional DynamicsDynamics

While the functions of the financial system are stable, the ways in which they are performed are not.

CommodizationTemporal pattern: the “successes” of new financial

products migrate from intermediaries to marketsOnce they are seasoned and perhaps after some

information asymmetries are resolved.Financial markets replace financial intermediaries

From opaque (financial companies) to translucent (funds) to transparent (markets)

Credit insurance replaced by put option on bonds (CDS)Securitization

Agent-type institutions compete with principle-type institutions

Financial-innovation spiralFinancial intermediaries create and test new products, then

move to market after standardization.The proliferation of new trading markets makes feasible

the creation of new custom-designed financial products that improve market completeness.

ExampleEurodollar futures market

Provides organized trading in standardized LIBOR deposits at various dates in the future.

Provides financial intermediaries with a way to hedge more efficiently custom-contracted interest-rate swaps based on a floating rate linked to LIBOR.

Eurodollar futures market becomes a great financial success.Swaps with relatively standardized terms began to move to

the market.These pure vanilla swaps expands the opportunity structure

for intermediaries to hedge, and to enable them to create more customized swaps.

Security InnovationsAn immutable set of financial functions

Why innovation?History from 1973 to 1993

Open interest on exchange-traded option contracts from 0.25 mln to 25 mln

From virtually no junk bonds issued to 50 bln outstanding in mid-1980s and to over 200 bln outstanding

From no swaps market in 1980 to 3 tln in interest-rate swaps

From 6 bln in MBSs outstanding to 2 tln

I. Costs1. Marketing

Identifying and educating buyers and sellers are labor- and information-intensiveDefined-benefit pension systems clientele: long-maturity

CMO tranches, zero-coupon bonds, portfolio insurance.Interest-rate swaps and basis (difference between LIBOR and

the prime rate) swaps to commercial banks.*

2. ManufacturingRaw materials

Using index futures rather than trading stock basket to replicate put for portfolio insurance

Assessable stocks: due to lack of information, shareholders provide committed cash to the firm only after regular assessments (milestone payments, secured debt, bond covenants).

Technologies Computing, telecommunication and financial engineering theory

(dynamic replication): portfolio insurance, securitization (thousands of small and constantly changing receivables), cross-border arbitrage.

Legal: no loophole to circumvent the original intent.

3. Taxes and regulations ARPPS & MMP: debt-like return with intercorporate dividend

exclusion Tax-deductable equity

US Banks offer Eurodollar CDs to circumvent reserve requirements

Insurance companies purchase index-linked bonds to circumvent regulatory constraints.

Perpetual floating rate note to meet capital standards.Deregulation of the natural gas market lead to Enron Gas

Service’s natural gas derivatives market.

II. Changing demands1.Life cycles

College costs linked investmentsVenture leases: sales-leaseback of patents for biotech firms.LBO: deferred-cash-flow instruments.

2. Volatility (exogenous shocks) Lowers marketing cost Increases the dispersion of beliefs and the potential for arbitrage Broadening of the potential market Cessation of governmental control

Inflation-indexed bonds Legal tender bonds: gives the payer the option of paying in any kind of legal

tender

III. Experimentation An evolutionary story of innovation, learning and

experimentation Legal language cannot fully define all rights or the interpretation of

rights

Virtually no patent protection (reverse engineering)Regulators close the loopholesIncome bonds

Failure to pay interest was a condition of default only if the firm had sufficient profits

Provide financing for distressed firmsEnjoy tax advantages of debt without threatening financial

distress.*But the non-cumulative feature allows firms to shift income to

the detriment of bondholders (concentrating income in one period and no income for all other periods)

Accounting manipulation by expensing capital investments even if cumulative.

Subsequent income bonds added cumulative features and carefully prescribed methods of computing earnings, even participation features and voting rights.

Early warrantsSecurities designed to sell investors the upside, bonds with

warrants.No protection against cash and stock dividends or splits.

Modern preferred stocksProvide investors with a substitute for commercial paper, but

was structured as equity to enjoy dividend income exclusion by corporations.

Assured of virtually no potential principal losses from interest rate risk.

Adjustable-rate perpetual preferred stock (ARPPS): paid a market rate of dividends, adjusted every 49 days (minimum holding period to obtain favorable tax treatment).

But credit of the issuer could deteriorate or credit spreads could widen.

Counter factorsProduct proliferation may make it more costly to sell

new productsAvailability of exchange-traded products may stifle

traditional innovationWell publicized disasters could lead to a backlash

against innovation

Future ImplicationsFinancial institution

Forces: lower costs & increasing global competitionLay the foundation for a substantial increase in both

the frequency and the magnitude of the changes in the institutional structure.

Applies also to the regulatory bodies that govern financial firms.

The long-run role of regulatory change as an exogenous force for financial innovation is limited.*

ParticipantsCorporations

Sophisticated hedging and risk management will become an integrated part of the corporate capital budgeting and financial management process.

The posting and careful monitoring of collateral is likely to be more widely adopted as the primary means for ensuring counterparty performance.*

HouseholdsMove away from direct trading in individual stocks or bond

where they have the greatest comparative disadvantage (diversification, trading cost, information) toward aggregate bundles of securities

Cause liquidity to deepen in the basket/index securities while individual stocks to become relatively less liquid.

Less need for the traditional regulatory protections and other subsidies of the costs of retail investors.

The emphasis on disclosure and regulations will tend to shift up the security-aggregation chain to the interface between investors and investment companies, asset allocators, insurance and pension products.*

Regulators Policies and regulations should facilitate the

requisite changes in structure instead of attempting to protect and preserve the existing ones.

Explicit recognition of the interdependence between product and infrastructure innovations and of the inevitable conflicts that arise between the two.

At times, the imbalance could become large enough to jeopardize the functioning of the financial system.

Change the format of regulation from institutional to functional.Promoting competitionEnsuring market integrity including macro credit risk protections

(market breakdown)Managing public-good type externalities*

International issue of the tradeoff between the benefits of regulatory cooperation and the benefits of regulatory competition.

The Structure of Interest Rates#• Yield curve

– How the yields on U.S. government debt obligations vary with maturity.

• The yield has little to do with any rate of interest that can actually be realized in the market.

– Has to assume the same constant reinvest rate.

1 / 1 2(1 ) (1 ) (1 ) ...2 2 2 2 2

(1 ) (100 )2 2 2

cN d d N Nb b b

b

r r rC CP

rC C

• Strip yield curve– The actual structure of interest rate

• Yields on debt obligations promising a single future payment (pure discount or zero coupon bonds).

– Can actually be earned if held to maturity.– Coupon bonds can be thought of as a bundle or

portfolios of pure discount bonds.

1 2 3 4

1 2 3

4,

1 21 2

1 2

Let , , , be four coupon bonds with maturities0.5, 1, 1.5, and 2 years as well as coupons , , , and respectively. Let denote strip yield. We know

/ 2 100 / 2; 1 / 2 1

s

b b

P P P PC C C

C r

C CP Pr r

22

2

/ 2 100 , and so on./ 2 (1 / 2)b

Cr

– Yield to maturity is actually a complex average of strip yields. The schedule of strip yields implied by the prices of coupon bonds is called the spot yield curve.

– The explicit yields associated with the STRIP market are referred to as the strip yield curve.

– If the spot curve is rising (falling), then yield curve will also be rising (falling) but less than the spot curve, i.e., flatter (lower slope).

2 21 1 2 22

1 2

3 3 33 32 3

1 2 3

/ 2 / 2 100Then . Solve to get ,(1 / 2) (1 / 2)

/ 2 / 2 / 2 100 to get and so on.1 / 2 (1 / 2) (1 / 2)

s b ss s

ss s s

C Cr r P rr r

C C CP rr r r

– In practice, the spot curve and the strip curve may differ for a number of reasons including taxes, bid-ask spreads or non-market prices.*

• Forward rates

• Strip yields are actually geometric average of the current spot rate and forward rates. When forward rates are rising (falling), strip yields will also be rising (falling).

222 1

3 2 33 23 2 1

2 3

Implicit forward rates can be drived from strip yields.

(1 ) (1 ) (1 ), and2 2 2

(1 ) (1 ) (1 ) (1 ) (1 ) (1 )2 2 2 2 2 2

is simialr to a 6x12 FRA and a 12x18 FRA.

fs s

f f fs s s

f f

rr r

r r rr r r

r r

– The implicit forward rates may not be equal to the expected future spot rate unless the unbiased expectation hypothesis holds.

• Case– COUGARs (79-86)

• Arbitrage among yield curve, spot yield curve, strip yield curve, and forward rates with all-in costs.

1 2

22 1 1 2

1 2 2

Let be the six month strip yield six month from now, if the Expectation Hypothesis holds, then

(1 ) (1 ) [1 ( )], hence,( )

s

s s s

s f

r

r r E rE r r

Duration and Convexity• Duration

– PVs of cash flows weighted average time• Linear approximation to a bond’s price-yield

curve.• For zeros, the maturity is the “average life”.• Longer-lived bonds are more sensitive to rate

changes than shorter-lived bonds.2

1

/(1 / 2)2

tTt b

t

C rtDP

2 21

1 1

2

1

(1 ) , (1 ) ,2 2 2

/(1 / 2)/ /(1 / 2)2

* (modified duration)(1 / 2)

Hedging a long position of a 9-year bond by selling short a 3-yea

T Tt tb b

t tt tb

tTt b

btb

b

r rP tP C Cr

C rP P t rr P

D Dr

9 9 39 3 9 3

3 9 3

** *9 9 99 3 *

3 3 3

r bond, the hedge ratio is

(assume = ) , ,

- , hence,

b bP P Pr r P h P hP P P

P P DD h D hP P D

– Shortcomings of the duration hedge ratio• The yield curve does not always shift in parallel fashion, i.e., it

is not true that changes in short-term and long-term rates are equal.

• Rates sometimes jump (convexity)– The hedge will be imperfect for large rate movements,

even if the rates on both bonds change identically. One bond may have a curvier price-yield profile than the other.

– Addressing the convexity issue is of crucial importance in dealing with bond options and other instruments that contain option features (mortgage and callable bonds*).

9 3

9 9 3 3

9 3

9 9 9 9 3 3 3

3 9 3

* *9 9 39 3

3

9

3

If but both are subject to the same

single factor , then ,

/ / ,

,

/ hence, /

b b

b b

b b

b b b b

b b

b

b

r rr P r Pr hr r r r

r P P r r P rhr P P r Pr P rD h Dr P r

r r Phr r

*9 9

*3 3

DP D

• Convexity– Explanation for an inverse yield curve

• Expectations for inflation in the distant future may be less than those for the near future.

• The relative demands for different maturities may be determined by institutional factors and, because players don’t like to move out of their preferred maturity, e.g., insurance companies need to hedge their positions on long-term retirement contracts; treasury debt retirement policies that reduce the supply of long bonds (preferred habitat). Reduced demand for long-term funds for consumption and investment.

• Artifact of monetary policies: Fed reduces interest rate to expand the economy pushing up inflationary expectation and vice versa.

• The yield to maturity may not show all the gains that can be realized from holding a long bond.

– The convexity of a long bond relates to yield volatility. A delta neutral portfolio can be put together for long maturity bonds to benefit from volatility shifts.*

– Research findings for inverse yield curves• The end of an economic boom and the start of an economic

bust? Not a sufficient condition.– Recession followed 4-6 quarters later.– 10-year vs. 2-year TB rates (early signal), 10-year vs 3-

month TB rates (best forecaster) , and 10-year TB rate vs. Federal fund rate (reflecting monetary policies, not a very good indicator).

• Exceptions– Credit crunch (1967) caused short-term rates to

jump temporarily.– Russian financial crisis (1998) caused investors

to seek safer US long-term TBs.• False exception

– Budget surplus in 2000 reduced US TB supply, but turn out to be a recession.