Welcome to the
Financial Engineering Practitioners Seminar
Series
Speaker: Prof. Philip Maymin
Sponsored by:
Any Regulation of Risk Increases Risk
Presentation by Philip Maymin
Joint work with Zak Maymin
Columbia IEOR
Financial Engineering Practitioners Seminar
September 15, 2014
Any Regulation of Risk Increases Risk
(not legislation)
Approaches:
Mathematical
Empirical
Experimental
Algorithmic
(systemic risk)
Regulation vs. Legislation
What’s the Difference?
1. Legislation is what you’re supposed
to do and regulation is how you are
supposed to do it.
2. Elected officials make legislation,
appointees make regulation.
3. Basically no difference.
Regulation vs. Legislation
• Legislation:
– 2009 United States Code:
38,712 pages, 6 feet of shelf space.
• Regulation:
– 2007 Code of Federal Regulation:
145,816 pages, 25 feet of shelf space.
– 2008 Federal Register:
80,700 pages
(these are changes).
Photos from http://extent-of-regulation.dhwritings.com/
Regulation vs. Legislation
Histogram of Laws per Regulation
Histogram of Regulations per Law
Data source: Government Printing Office, Parallel Table Of Authorities And Rules
Do Risk Regulations Work?
BACKFIRE ?
WORK ?
NOT
WORK ?
Image Sources: http://www.thirdage.com/image/businessmantightrope
http://www.damaideparte.ro/index.php/asumarea-riscurilor/359/
http://ent12cooper.blogspot.com/2010/09/embracing-risk.html
The Problem
The “Solution”
Why Did You Pick Your Bank?
1. Offered safety and the absence of risk.
2. Location of branch.
3. Connection through work, or a personal
relationship, or friend recommended.
4. Low fees or high rates,
or many different services.
How People Choose Banks
The Fed and the IRS: Survey of Consumer Finances
What Would Banks Do?
Enter: Regulators
What Would YOU Do, If You Were a Bank?
Part I
Say there are two otherwise identical assets.
But asset 1 has a lower regulatory risk
requirement.
Which would YOU buy?
1. Buy asset 1
2. Buy asset 2
What Would YOU Do, If You Were a Bank?
Part II
Say asset 1 is essentially a leveraged version
of asset 2, e.g. asset 1 = 1.1 * asset 2.
But asset 1 and asset 2 have the same
regulatory risk requirement.
Which would YOU buy?
1. Buy asset 1
2. Buy asset 2
What’s a Basel?
• The Basel Committee on Banking Supervision
• A group of top global economists
• Working together to define standards
• That are recommended to the BIS
(Bank for International Settlements)
• Which then flow down to the member states
and their own central banks
A Rough History of Risk Regulation
• Constant amounts
depending on asset class
• Value-at-Risk (VaR)
measures
• Combination of VaR and
Stress VaR
• Basel I
• Basel II
• Basel 2.5,
Basel III
Values-at-Risk
•
•
•
•
Value-at-Risk
Basel, BIS, Fed
Volatility
Standard Deviation
3 times the 10-day 99% VaR ≈
3 10 ⋅ 2.33 ⋅ 𝜎 =
22𝜎
Assets are Riskier than they Appear
For 1000 securities and 60 months of (normal)
10 securities to exhibit
returns, we should expect ___
volatility less than 80% of their true value?
Month 1
Month 2
…
Month 60
Volatility
Security 1
𝑅1,1
𝑅1,2
…
𝑅1,60
𝜎1
Security 2
𝑅2,1
𝑅2,2
…
𝑅2,60
𝜎2
…
…
…
…
…
Security 1000
𝑅1000,1
𝑅1000,2
…
𝑅1000,60
𝜎1000
𝜎𝑖2 =
12
60
2
𝑅𝑖,𝑡
𝑡
Assets are Riskier than they Appear
Conditional Expected Value
of Sample Standard Deviation
Suppose 𝑦𝑖 , 𝑖 = 1,2, … , 𝑛, are independent and identically distributed
𝒩 𝜇, 𝜎 2 normal returns and the sample standard variances 𝑠𝑛2 are
defined as usual by:
𝑠𝑛2 =
1
𝑛−1
𝑛
𝑖=1
𝑦𝑖 − 𝑦
2
, where 𝑦 =
1
𝑛
𝑛
𝑖=1 𝑦𝑖
.
We derive a closed-form solution for the conditional expected value
of the sample standard deviation as a percentage of the true standard
deviation for any tail probability 𝛼:
𝐸 𝑠𝑛 𝑠𝑛 ≤𝑠𝑛,𝛼 )
𝜎
𝑛
Γ 2
where 𝐾𝑛 =
Γ
𝑛−1
2
1
𝑛−1 2
2
= 𝐾𝑛
2 ≤ 𝜒2
𝑃 𝜒𝑛
𝑛−1,𝛼
𝛼
Portion of true Sigma
for bottom 10%, 1%, and 0.1%
What about fat tails?
What about daily returns?
• Simulate fat tails with normal distribution, with all draws
within 𝜖 of zero replaced by a constant h of the same sign.
E.g. if 𝜖 = 0.01 and ℎ = 10, then −0.005 becomes −10.
• Calculate 1,000 sample
standard deviations for
1,260 periods, which is
equivalent to about
5 years of daily returns.
Stressed VaR
• Basel II, Basel 2.5, Basel III
• In addition to regular VaR, also add the
highest VaR that would have been calculated
during a historically stressful environment,
e.g. 2008-2009.
What about Stressed VaR?
• For same fat tailed distribution, for each asset, calculate
the sum of the five year standard deviation and the
highest rolling one year standard deviation. Then look at
the distribution over assets.
Even more assets
exhibiting ≤ 𝟖𝟎%
of average risk.
Future 5-year Vol / Past 5-year Vol
Future 5-year Vol / Past 5-year Vol
Future 5-year Vol / Past 5-year Vol
Future 5-year Vol / Past 5-year Vol
Experimental Results (Gedanken)
• Flip a coin ten times.
• Count the number of heads.
• What do you think will happen with your next ten
flips?
– Expected Profit: # heads
– Risk: Square root of (# heads) * (10 – #heads) / 10
– Sharpe Ratio: Expected Profit / Risk
• Now all banks invest in the few low-risk coin tossers.
– So not only does each individual bank’s risk go up, but
systemic risk goes up.
Informal Algorithmic Intuition
• Imagine a portfolio Π of investments that:
– Generate outsized returns in general
– Crash during times of systemic collapse
• Regulated banks incentivized to tend towards Π
• By definition, Π not historically detectable a priori
• Objective regulation cannot prevent Π because it
is effectively defined by overconcentration
• Subjective regulation may prevent Π but violate
the rule-of-law
Any solutions?
• Results hold for any objective regulation of risk
– Not just Value-at-Risk or standard deviation.
• So risk must be subjectively measured.
• Two solutions:
– Complete nationalization of all banks
• Single central banker/risk manager decides however they want
– Complete deregulation of all banks
• No more deposit insurance. No more Federal Reserve.
• Probably no more demand deposits. (Depends on market.)
• Free market lets you put your money where you think it is safe.
A Bank in Every Garage
Links
• Technical Paper:
Maymin, Philip Z.; Maymin, Zakhar G. (2012), “Any
Regulation of Risk Increases Risk”, Financial Markets
and Portfolio Management 26:3, 299-313.
• Less Technical Papers:
– Maymin, Philip Z., “Why Financial Regulation is Doomed to Fail,”
Library of Economics and Liberty, March 2011,
http://www.econlib.org/library/Columns/y2011/Mayminfinancial.html
– Maymin, Philip Z.; Maymin, Zakhar G., “Viewpoints: An
Experiment in Risk,” American Banker, June 2010,
http://www.americanbanker.com/issues/175_106/vp-experiment-securities-risk1020284-1.html
– More at http://philipmaymin.com/academic-papers#risk