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© Uwe Wystup: On the Price of a Guaranty - page 1

On the Price of A Guaranty

A Statistical Comparison of the Returns of Long-term Investments

Uwe Wystup27 November 2007Wealth Management & Private Banking Conference, Amsterdam


Outline

Returns of classical funds Motivation for guaranty-productsHow the financial industry reacted Guaranty productsReturn comparisonChallenges for the next generation financial engineers


Classic Bond Fund

Templeton Global Bond Fund: Net Asset Value

0

50

100

150

200

250

300

350

400

Sep

-86

Sep

-88

Sep

-90

Sep

-92

Sep

-94

Sep

-96

Sep

-98

Sep

-00

Sep

-02

Sep

-04

Sep

-06

Time

Valu

e gi

ven

an in

itial

inve

stm

ent

of 1

00 E

uro

Source: Franklin Templeton. own calculations


Classic Bond Fund

Templeton Global Bond Fund: Return of rolling 5 year investments

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

Sep-

86

Sep-

87

Sep-

88

Sep-

89

Sep-

90

Sep-

91

Sep-

92

Sep-

93

Sep-

94

Sep-

95

Sep-

96

Sep-

97

Sep-

98

Sep-

99

Sep-

00

Sep-

01

Start of Investment

Con

tinuo

us a

nnua

l ret

urn

Log-Returns (EUR)rollingAverage 7.00%

Std.-Dev. 2.30%



Classic Stock Fund

Templeton Growth Fund, Inc. : Net Asset Value

0

5000

10000

15000

20000

25000

30000

35000

Nov

-54

Nov

-58

Nov

-62

Nov

-66

Nov

-70

Nov

-74

Nov

-78

Nov

-82

Nov

-86

Nov

-90

Nov

-94

Nov

-98

Nov

-02

Time

Valu

e gi

ven

an in

itial

inve

stm

ent

of 1

00 E

uro

100€ initial investment



Classic Stock Fund

Templeton Growth Fund, Inc. Returns of rolling 25 year investments

6.0%7.0%8.0%9.0%

10.0%11.0%12.0%13.0%14.0%15.0%16.0%

Nov

-54

Nov

-56

Nov

-58

Nov

-60

Nov

-62

Nov

-64

Nov

-66

Nov

-68

Nov

-70

Nov

-72

Nov

-74

Nov

-76

Nov

-78

Nov

-80

Start of Investment

Con

tinuo

us a

nnua

l ret

urn

Log-Returns (EUR) rolling

Average 12.42%

Std.-Dev. 0.97%



Retail investors are scared ofFictitious Scenario with Crashs

2000

4000

6000

8000

10000

12000

14000

16000

0 1 2 4 5 6 7 8 9 11 12 13 14 15 16 18 19 20 21 22 23 24

Time (years)

Valu

e of

the

Und

erly

ing

Source: own simulation


Retail investors are also scared of

Fictitious Scenario with Asset Melt Down

2000

7000

12000

17000

22000

27000

0 1 2 3 4 5 6 6 7 8 9 10 11 12 13 14 15 16 17 17 18 19 20 21 22 23 24 25

Time (years)

Valu

e of

the

Und

erly

ing

Source: own simulation


Reaction of the Financial Industry: Guaranty-Products

Funds

Investor is shareholder of the fund → no issuer default risk

Tenor: often fixed. long maturities

Certificates

Market risk

Issuer default risk

Tenor: short-term or mid-term. (up to 10 years)


Guaranty-ProductsCertificates in Germany (source: Stuttgart Exchange)

New way of thinking: Use certificates as investment strategy for retirement


Classifying the Types of Guaranty

Discount-Type: Up-trend-participation is limited by shorting a call option. The underlying sells at a discount.

Warning: No Guaranty at all!Bonus-Type: Dividends are kept by the issuer to buy a put option. Warning: Guarantee is often limited as the Put has a down-and-out barrier. Performance-Type: Zero-coupon bond with a coupon below the market risk-free and a call option on the index. CPPI-Type (Riester-Pension): Dynamic portfolio insurance model: as the index rises: invest more in the index – if the index declines: invest less in the index


CPPI

Initial amount: 100 EuroProtection level: 100 Euro Present value: 96 Euro

Buffer: 4 Euro (4 = 100 - 96 )

Equity quota: 20 Euro ( = 4 / 20%)Max Loss Assumption: -20%

(Allocation multiple: 5)Risk free quota: 80 Euro

( = 100 - 20)


CPPI

Equity : 20

Risk free portion: 80

Equity: 22

PV of Prot. Level: 96 Buffer: 4


PV of Prot. Level : 98 Buffer: 6

Portfolio value: 100 Portfolio value: 104

30

74

104

Equity market 100 Equity market 110 + 10%


CPPI

Equity : 30


Equity: 27




Portfolio value 104 Portfolio value: 102

15

87

102

Equity market 110 Equity market 99 - 10%

Discussion: Crash-Puts


Source: BVI turnover stats of 26.01.2007. own calculations

Wealth invested in Funds in Germany

-20

-10

0

10

20

30

40

50

2002 2003 2004 2005 2006Year

Net

wea

lth in

Bill

ion

Euro Other Funds (O)

Money Market Funds(MM)Hedgefonds (H)

Guaranty Funds (G)

Mixed Funds (M)

Bond Funds (B)

Stock Funds (S)


Simulation Model


So what’s a jump?

This week: Absolute Capital dropped by 65%

The largest drop of the Dow Jones Industrial Average Index was ______ in _____


ScenariosWorst CaseDAXBest CaseParameter

21.21.2Ø Jumps per year

-0.87%-0.87%-0.87%Ø Jump size

12.7%12.7%12.7%Ø Jump volatility

27%17.24%17.24%Ø Volatility

Asset Melt Down: 9.23% to -0.41% linear

9.23%11.5%Ø Return

1.68 to 0.00 linear1.68%1.68%Ø Dividend rate

Source: Yahoo Finance DAX history. own calculations

Jump: upper and lower 5% quantile of the monthly log-returnsExample: mid February – mid March 2007


Interest Rates

As of December 2006 How would you build a quick simulation for the future?

Euro-Termstructure

3.40%3.45%3.50%3.55%3.60%3.65%3.70%3.75%3.80%3.85%3.90%

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Maturity (in years)

Shor

t Ter

m R

ate


Results for 5 Year Investments

3.02%

2.76%2.72%0.85%

4.42%

3.35%

4.02%

5.51%

5.72%

Expected ReturnWorst Case

2.94%3.27%3.00%Performance

5.89%6.93%noneDiscount6.72%8.71%-3.86%Bonus

4.15%

9.23%

7.00%

8.04%

11.02%

11.43%

ExpectedReturnNormal Case

ExpectedReturnBest Case

Guaranteed Return

Product

9.00%noneBond Fund (Global Bond)

11.50%noneIndex (DAX)

5.69%0.00%CPPI

13.43%noneStock Fund (Templeton Growth)

13.02%noneStock Fund (Mutual Shares)

10.04%noneMixed Fund (Income)

5000 simulations

2.60%

-8.06%

-13.0%

-0.87%

Minimum


Result for 25 Years: Guaranty costs about half the Return

3.20%

3.25%3.00%2.42%

4.42%

3.65%

4.25%

6.37%

6.21%

Expected ReturnWorst Case

4.44%6.02%3.00%Performance

6.62%7.57%noneDiscount6.10%8.24%2.81%Bonus

5.26%

9.23%

7.60%

8.50%

12.73%

12.42%

Expected ReturnNormal Case

Expected ReturnBest Case

Guaranteed Return

Product

9.60%noneBond Fund (Global Bond)

11.50%noneIndex (DAX)

7.46%0.00%CPPI

14.42%noneStock Fund (Templeton Growth)

14.73%noneStock Fund (Mutual Shares)

10.73%noneMixed Fund (Income)

5000 simulations

4.56%

9.37%

9.86%

Minimum

Discuss: Politics & Capital Guarantee


Source: own simulation and calculations

Comparison of 25 Year Investments - Guaranty vs. Classic Investment -

0%

5%

10%

15%

20%

Sto

ck F

und

(Tem

plet

onG

row

th)

Sto

ck F

und

(Mut

ual S

hare

)

Mix

ed F

und

(Inco

me)

Bon

d Fu

nd(g

loba

l Bon

d)

Inde

x (D

AX)

Dis

coun

t-Typ

e

Bonu

s-Ty

pe

Perfo

rman

ce-

Type

CPP

I-Typ

e

Type of Investment

Ret

urn

MaximalExpectedMinimal

Guaranteed


Portfolio International, September 2007


Handelsblatt 26.10.2007


Discussion in the Media

CPPI-Type normal case - no fees

5.00%5.50%6.00%6.50%7.00%7.50%

-3.0

0%

-2.5

0%

-2.0

0%

-1.5

0%

-1.0

0%

-0.5

0%

0.00

%

0.50

%

1.00

%

1.50

%

2.00

%

2.50

%

3.00

%

guaranteed return

expe

cted

retu

rn

… depends heavily on where we are on the x-axis and …


… and heavily on the fees

CPPI-Type normal case - with fees

2.50%

3.50%

4.50%

5.50%

-3.0

0%

-2.5

0%

-2.0

0%

-1.5

0%

-1.0

0%

-0.5

0%

0.00

%

0.50

%

1.00

%

1.50

%

2.00

%

2.50

%

3.00

%

guaranteed return

expe

cted

retu

rn

Red dots: 99% confidence interval


Advantage of a Guarantee as a Function of Investment Period

today 5 years 25 years

Crash-RiskAsset Melt Down Risk

Guaranty justifiable

Crash-Risk

Asset Melt Down Risk

Full Protection: Savings AccountPartial Protection (Riester-Pension): Return-Cruncher

Ideal: Global Stock Portfolio = Index


In short: At retirement an investor without full-protection will probably be six times as rich as his security-fanatic neighbor.

Wind-up: Investing 1,000 EUR today yield:

today 5 years 25 years

22,3091,860TempletonGrowth

3,7241,300Guaranty-Fund (5% Return expected)


Quantitative Challenges in Derivatives for the Next Generation of Financial Engineers

Long-term options pricing: Benchmark approach to quantitative finance (Platen/Heath)Merging Asset Management with standard derivatives markets: in particular: under which measure should one work, i.e. real world vs. risk-neutral

Long-term exotic option pricing. How to extend models from vanilla to exotic options.

Invention of useful long-term investment contracts with guaranty and client-oriented flexibility, e.g. max-level option of DWS

QP ↔


Uwe Wystup

CEO MathFinance AG

Professor of Quantitative Finance Frankfurt School of Finance & Management

http://www.mathfinance.comPhone/Fax +49-700-MATHFINANCEE-Mail: [email protected]

Books, Articles, Presentations and CV:http://www.mathfinance.com/wystup/


Jürgen Hakala and Uwe WystupForeign Exchange RiskRisk Publications, London 2002 http://www.mathfinance.com/FXRiskBook/

Uwe WystupFX Options and Structured ProductsWiley Finance, 2006http://fxoptions.mathfinance.com/

Selected Publications

Efficient computation of option price sensitivities using homogeneity and other tricks, joint with Oliver Reiss, The Journal of Derivatives Vol. 9 No. 2, Winter 2001

Valuation of exotic options under short selling constraints, joint with Steven E. Shreve and Uwe Schmock, Finance and Stochastics VI, 2 (2002)

The market price of one-touch options in foreign exchange markets, Derivatives Week Vol. XII, no. 13, London 2003

Efficient computation of option price sensitivities for options of American style, joint with Christian Wallner, Wilmott. 2004

The Heston Model and the Smile, joint with Rafal Weron, Chapter contribution to the book Statistical Tools for Finance and Insurance (STF), eds. Pavel Cizek, Wolfgang Haerdle, Rafal Weron. 2004.


Services of MathFinance

FX Option Pricer DLL/XLL with market prices following the cost of volatility hedging. Vanilla, Digital, OneTouch/NoTouch, DoubleOneTouch/DoubleNoTouch, Single Barrier (European and American), Double Barrier, Window Barrier, Faders

Certificate ratings, independent studies and statistical surveys

Tailor made prototypes of pricing and hedging tools for derivatives in visual basic, c/c++, Mathematica

Consulting on FX options and structured products: pricing, hedging, applications in treasury management

Training Courses in Derivatives, specially our area of expertise: FX Options.

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