Download Innovation in the Asset Management Industry: Risk

Innovation in the Asset Management Industry:
Risk Measurement and Risk Management
The European Colloquia 2010, London
Robert C. Merton
Harvard Business School
European Colloquia Series: Towards a New Architecture
London
January 28, 2010
Domain of Investment Management: Stages
of Production Process
Passive
Well-Diversified
Efficient
Portfolio
“Efficient Exposures”
Active
Asset-Class
Allocation
Macro Sector
Market Timing
Superior Performing
Micro Aggregate
Excess-Return
Portfolio
“Alpha Engines”
Super
Efficient
Portfolio of
Risky Assets
(Optimal
Combination of
Risky Assets)
Riskless
Asset
Portfolio
• Components of
Best Performing
Risky Assets
Only Portfolio:
•Risk Modulation
through Hedging or
Leveraging
•Diversification
Risk Modulation
•Market Timing
Active Management
Copyright © 2010 by Robert C. Merton
Optimal
Portfolio of
Assets
Alter Shape of
Payoffs on
Underlying
Optimal Portfolio
Structured
Efficient Form
of Payouts to
Client
Client
Households
Entrepreneurs
Endowment
Corporation
(Derivative
Securities with
Non-Linear
Payoffs)
• Risk Modulation
through Insurance
or non-linear
leverage
• Tax efficient
• Regulatory efficient
• Liquidity allocation
• Pre-programmed
dynamic trading
• “Building Block”
State-Contingent
Securities to create
specialized payout
patterns
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Generating Superior Investment Performance:
What is Alpha?
Traditional Alpha-Seeking
•
•
•
•
Depends on being faster, smarter, better models or better information-inputs
Is it sustainable? Is it scalable?
The Cost of Active Investing
Non-economic costs and benefits
Alpha which becomes Specialized Beta
•
•
•
Performance improvement over benchmark which can be replicated by passive
strategies
Hedging needs of classes of Investors: Interest rate, volatility changes, liquidity, human
capital
Momentum, liquidity-event risk, small cap vs. large cap stocks, value vs. growth stocks
Financial-Services Alpha
•
•
•
•
Institutional rigidities: regulations, charter, accounting, tax
Depends on being lightly regulated, strong credit-standing, long-horizon, flexible liquidity
needs, large pool of assets, reputational capital and sponsorship value
Is it sustainable? Is it scalable?
Is it a comparative advantage of the provider of the service?
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Copyright © 2010 by Robert C. Merton
Calculating “True” Fees for Alpha:
Performance and Alpha/Beta Mix
Pre-fee Return on Portfolio: R  R f     RM  R f   w    
w  fraction in “pure” alpha and wM = fraction in “pure” beta
= fraction in benchmark
= 
Volatility “scale” active portfolio, so that it has same total volatility as benchmark
#1 Annual Fee (2%, 20%) = 2.0% + .2 Call (  2 , dividend = 2%, r, E = 1)
#2 Annual Fee (1.25%, 20%) = 1.25% + .2 Call (  2 , dividend = 1.25%, r, E = 1)
 M = 15% r = 5%
Fee Paid #1 = 3.47%

w  1   2
0.000
0.300
0.500
0.658
0.700
0.800
0.900
1.000
1.000
0.954
0.866
0.810
0.714
0.600
0.436
0.000
Fee Paid #2
2.81%
2.95%
3.24%
3.46%
3.93%
4.68%
6.45%

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Copyright © 2010 by Robert C. Merton
Effects of Infrequent Trading and Stale Prices
on Performance Measurement S&P 500 Weekly
Returns January 1995-December 1999
Average
Annual
Arithematic
Return
Annual
Standard
Deviation
Correlation
with
S&P 500
Beta
Alpha
S&P 500 (0
week no trade)
24.3%
14.9%
1.000
1.000
0.0%
S&P 500 (1
week no trade)
24.0%
14.1%
0.486
0.460
9.9%
S&P 500 (2
week no trade)
24.3%
14.8%
0.329
0.324
12.7%
S&P 500 (3
week no trade)
24.2%
15.3%
0.253
0.259
13.8%
(0 week no trade) means the security trades (or is marked) once every week
(1 week no trade) means the security trades (or is marked) once every two weeks
(2 week no trade) means the security trades (or is marked) once every three weeks
(3 week no trade) means the security trades (or is marked) once every four weeks
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Copyright © 2010 by Robert C. Merton
Estimated Beta (β)
Weekly Returns January 1995 - December 1999
Security: Standard & Poor’s 500
1.25
1.00
0.75
0.50
0.25
0
1
2
3
Number of Nontraded Weeks
per Traded Week
Estimated Alpha (α)
0.00
15%
10%
5%
Number of Nontraded Weeks
per Traded Week
0
1
2
3
0%
Copyright © 2010 by Robert C. Merton
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Private Equity & Other Non-Traded Assets: Performance & Risk
Gompers and Lerner 1974-1997: Sensitivity to Wrong Systematic Risk Estimate
Returns
All Private Equity
S&P 500
Risk-Free Rate
If Beta = 0, Alpha
14%
16%
6%
+8%
If Beta = 1.42, Alpha
- 6%
Core Problem: Mark-to-Market versus Non-Trading Accounting values are
subject to time lags and smoothing that completely destroys correlation among
measured asset returns. Indeed, asset returns have nil serial correlation in
practice so that covariance between Return at time t and Return at time t+1
day=0 for the same asset. Non-trading thus artificially creates a smaller beta.
Gompers-Lerner attempt to rectify with time series of returns as surrogate to
actual trading using best estimate of change in price from observable data.
More advanced approach would be a Brownian Bridge estimation model.
Another example: Real Estate Investment Trusts (REITS) versus Direct
Investment in Commercial Real Estate Fund.
Copyright © 2010 by Robert C. Merton
7
Risk Measurement for Credit-Risk Assets: Nonlinear Risks
of Being a Lender When There is Risk of Default
RISKY DEBT + GUARANTEE OF DEBT = RISK-FREE DEBT
RISKY DEBT = RISK-FREE DEBT - GUARANTEE OF DEBT
Corporation
Operating Assets, A
Debt (face value B), D
Common Stock, E
A=D+E
IN DEFAULT, THE HOLDER OF THE GUARANTEE RECEIVES PROMISED VALUE OF
THE DEBT MINUS VALUE OF ASSETS RECOVERED FROM DEFAULTING ENTITY =
MAX [0, B – A]
VALUE OF GUARANTEE = PUT OPTION ON THE ASSETS OF BORROWER
CREDIT DEFAULT SWAPS ARE GUARANTEES OF DEBT AND THEREFORE ARE PUT
OPTIONS ON THE ASSETS OF THE BORROWER
Copyright © 2010 by Robert C. Merton
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Non-linear Credit Risk Buildup
Firm/Mortgage
Corporate/Household Sector
Debt
Liability
DC
DC
D 'C
Corporate/Housing Assets, A C
Firm/Mortgage
Debt
Guarantee
Banking System
Liability
A 'C
AC
Government
Bank
Deposit
Liability
Guarantee
GB
GC
G 'C
G 'B
GC
GB
A 'C
Copyright © 2010 by Robert C. Merton
AC
Corporate /Housing Assets, AC
A 'B
AB
Bank Assets, AB
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Performance Measurement: Market Timing and
Nonlinear Risk Hedge Funds
Market Timing [A “free” call or a “free” put]
For Perfect Market Timing and No Borrowing or Short-Selling
R p  R f  Max O, Rm  R f 
 Rm  R f  Max O, R f  Rm 
Measuring Return to Market Timing


R p  R f  a  b Rm  R f  c Max O, Rm  R f   e p


R p  R f  a  b Rm  R f  c Call Return  e p
Hedge Fund Relative-Value Strategy [risk level change is negatively
correlated with returns]


R p  R f  a  b Rm  R f  c Call Return  e p
Hedge Fund Momentum/Stop-Loss Strategy [risk level change is positively
correlated with returns]


R p  R f  a  b Rm  R f  c Call Return  e p
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Copyright © 2010 by Robert C. Merton
Beyond VAR: Put Option Price for the Portfolio
as a Tail-Risk Indicator
Value-at-Risk (VaR): Summary Risk Measure
V(h)
(p, h) V(0) (h)
What is the minimum value of our portfolio at the end of time h with probability
1 – p? V (p, h)
What is the amount that the portfolio could lose it or more with probability p at
the end of time h?
VaR (p, h) = V (0) – V (p,h)
Put Option Price Reflects Rare-But-Significant Events
• Robust with respect to probability distribution
• Intuitive because the put price is the price of insuring the downside tail
• Reflects a price for insurance versus self-insurance amount of capital
• Jarrow and Van Deventer, GARP Risk Professional, August 2009
Copyright © 2010 by Robert C. Merton
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Integrated Systemic Risk Policy: Refinancing
Ratchet Effect 1996-2006
•
•
•
•
•
Trend #1: rising U.S. home prices
Trend #2: declining U.S. interest rates
Trend #3: increasing efficiency of mortgage refinancing
Each trend taken individually is beneficial or benign
All three trends superimposed creates unintended
synchronization of homeowner leverage
• Leveraging can be done incrementally, but deleveraging
cannot due to indivisibility of owner-occupied residential
housing
• Result: residential mortgage market is six times more
vulnerable and estimated losses of $1.2 - $1.5 trillion
between June 2006 and December 2008
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Copyright © 2010 by Robert C. Merton