© 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
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Outline
Returns of classical funds Motivation for guaranty-productsHow the financial industry reacted Guaranty productsReturn comparisonChallenges for the next generation financial engineers
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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
© Uwe Wystup: On the Price of a Guaranty - page 5
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%
Source: Franklin Templeton. own calculations
© Uwe Wystup: On the Price of a Guaranty - page 6
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
Source: Franklin Templeton. own calculations
© Uwe Wystup: On the Price of a Guaranty - page 7
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%
Source: Franklin Templeton. own calculations
© Uwe Wystup: On the Price of a Guaranty - page 8
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
© Uwe Wystup: On the Price of a Guaranty - page 9
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
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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)
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Guaranty-ProductsCertificates in Germany (source: Stuttgart Exchange)
New way of thinking: Use certificates as investment strategy for retirement
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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
© Uwe Wystup: On the Price of a Guaranty - page 13
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)
© Uwe Wystup: On the Price of a Guaranty - page 14
CPPI
Equity : 20
Risk free portion: 80
Equity: 22
PV of Prot. Level: 96 Buffer: 4
Risk free portion: 82
PV of Prot. Level : 98 Buffer: 6
Portfolio value: 100 Portfolio value: 104
30
74
104
Equity market 100 Equity market 110 + 10%
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CPPI
Equity : 30
Risk free portion: 74
Equity: 27
PV of Prot. Level: 98 Buffer: 6
Risk free portion: 75
PV of Prot. Level: 99 Buffer: 3
Portfolio value 104 Portfolio value: 102
15
87
102
Equity market 110 Equity market 99 - 10%
Discussion: Crash-Puts
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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)
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Simulation Model
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So what’s a jump?
This week: Absolute Capital dropped by 65%
The largest drop of the Dow Jones Industrial Average Index was ______ in _____
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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
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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
© Uwe Wystup: On the Price of a Guaranty - page 22
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
© Uwe Wystup: On the Price of a Guaranty - page 23
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
© Uwe Wystup: On the Price of a Guaranty - page 24
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
© Uwe Wystup: On the Price of a Guaranty - page 25
© Uwe Wystup: On the Price of a Guaranty - page 26
Portfolio International, September 2007
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Handelsblatt 26.10.2007
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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 …
© Uwe Wystup: On the Price of a Guaranty - page 29
… 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
© Uwe Wystup: On the Price of a Guaranty - page 30
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
© Uwe Wystup: On the Price of a Guaranty - page 31
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)
© Uwe Wystup: On the Price of a Guaranty - page 32
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: On the Price of a Guaranty - page 33
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/
© Uwe Wystup: On the Price of a Guaranty - page 34
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.
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