to Control Financial Risk

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(2) The Portfolio

Describes the portfolio composition, leverage, and risk exposure.

(3) Value At Risk

Introduces VAR as a method to control risk.

(4) Questions

Shows how VAR could have been applied to the OC portfolio.

(5) Epilogue

Discusses the recovery of Orange County and the impact of the bankruptcy on financial markets.

This loss was the result of unsupervised investment activity of Bob Citron, the County Treasurer, who was entrusted with a $7.5 billion portfolio belonging to county schools, cities, special districts and the county itself. In times of fiscal restraints, Citron was viewed as a wizard who could painlessly deliver greater returns to investors. Indeed, Citron delivered returns about 2% higher than the comparable State pool. Plot Citron's track record (Figure 1).

Citron was able to increase returns on the pool by investing in derivatives securities and leveraging the portfolio to the hilt. The pool was in such demand due to its track record that Citron had to turn down investments by agencies outside Orange County. Some local school districts and cities even issued short-term taxable notes to reinvest in the pool (thereby increasing their leverage even further). This was in spite of repeated public warnings, notably by John Moorlach, who ran for Treasurer in 1994, that the pool was too risky. Unfortunately, he was widely ignored and Bob Citron was re-elected.

The investment strategy worked excellently until 1994, when the Fed started a series of interest rate hikes that caused severe losses to the pool. Initially, this was announced as a ``paper'' loss. Shortly thereafter, the county declared bankruptcy and decided to liquidate the portfolio, thereby realizing the paper loss. How could this disaster have been avoided?

The portfolio leverage magnified the effect of movements
in interest rates.
This interest rate sensitivity is also known as *duration*.
2.1 Define duration

The duration was further amplified by the use of *structured notes*.
These are securities whose coupon, instead of being fixed, evolves
according to some pre-specified formula.
These notes, also called derivatives, were initially blamed for the
loss but were in fact consistent with the overall strategy.

Citron's main purpose was to increase current income by exploiting the
fact that medium-term maturities had higher yields than
short-term investments.
On December 1993, for instance, short-term yields were less than 3%,
while 5-year yields were around 5.2%.
With such a positively sloped
*term structure* of interest rates, the tendency may be to increase
the duration of the investment to pick up an extra yield.
This boost, of course, comes at the expense of greater risk.
Plot the term structure on December 1993
(Figure 2).
Display term structure of interest rates as of last week:
Bloomberg.

The strategy worked fine as long as interest rates went down. In February 1994, however, the Federal Reserve Bank started a series of six consecutive interest rate increases, which led to a bloodbath in the bond market. The large duration led to a $1.6 billion loss. Plot the path of interest rates to December 1994 (Figure 3). Graph interest rates: Federal Funds.

Based on firm scientific foundations, VAR provides users with a summary measure of market risk. For instance, a bank might say that the daily VAR of its trading portfolio is $35 million at the 99% confidence level. In other words, there is only one chance in a hundred, under normal market conditions, for a loss greater than $35 million to occur.VAR is the maximum loss over a target horizon such that there is a low, prespecified probability that the actual loss will be larger.

This single number summarizes the bank's exposure to market risk as well as the probability of an adverse move. As importantly, it measures risk using the same units as the bank's bottom line---dollars. Shareholders and managers can then decide whether they feel comfortable with this level of risk. If the answer is no, the process that led to the computation of VAR can be used to decide where to trim risk.

No doubt this is why regulators and industry groups are now advocating
the use of VAR systems.
Bank regulators, such as the
Basle Committee on Banking Supervision,
the
U.S. Federal Reserve,
the European Union's
European Commission (EC),
and Britain's
Bank of England
have converged on VAR as an acceptable risk measure.
For investments in mutual funds,
the European Commission (EC) and
the Securities and Exchange Commission (SEC)
are allowing the use of derivatives provided their risk is measured using VAR.

**Other Sites with VAR Information**

Perhaps the most notable of private-sector initiatives toward better risk management is that of J.P. Morgan, which unveiled its RiskMetrics system in October 1994. Forecasts of risk and correlations for more than 400 assets were posted daily on the web site. This allowed users to compute a portfolio VAR using the Delta-Normal method based on a 95% confidence level over a daily or monthly horizon.

There is a growing army of vendors who provide software ranging from
Excel add-ons to million-dollar firm-wide risk management systems.
For instance, visit the sites of
MSCI (formely RiskMetrics),
FIS Global (formely Sungard Risk Systems).

and
SS&C (a hedge fund administrator that acquired Algorithmics).
Among consultants,
Capital Market Risk Advisors
are well known.
Indeed, this New York consulting firm was hired November 3, 1994, to
dissect the Orange County portfolio.
Within a week, CMRA warned the county that the pool had already lost
$1.5 billion.
The firm now specializes in the valuation of complex portfolios, and in
"financial forensics"--analyzing sources of financial losses.

There is even an association of risk management professionals, the Global Association of Risk Professionals, which provides a forum for the exchange of information and education in the area of financial risk management. GARP administers the "Financial Risk Manager" certification upon successful completion of an examination.

** (1) Duration approximation.**

The effective duration of the pool was reported by the state
auditor as 7.4 years in December 1994.
This high duration is the result of two factors:
the average duration of individual securities of 2.74 years (most of the
securities had a maturity below 5 years), and the leverage of the
portfolio, which was 2.7 at the time.
In 1994, interest rates went up by about 3%.
Compute the loss predicted by the duration approximation and compare
your result with the actual loss of $1.64 billion.

** (2) Computation of portfolio VAR.**

(2) The yields data file
contains 5-year yields from 1953 to 1994.
Using this information and the duration approximation, compute the
portfolio VAR as of December 1994.
Risk should be measured over a month at the 95% level.
Report the distribution and compute the VAR:

- using a normal distribution for yield changes (Delta-Normal method),
and

- using the actual distribution for yield changes (Historical-Simulation
method).

Compare the VAR obtained using the two methods.

Download the "yields.xls" file.

** (3) Interpretation of VAR.**

- Convert the monthly VAR into an annual figure.
Is the latter number consistent with the $1.6 billion loss?

- From December 1994 to December 1995, interest rates fell from
7.8% to 5.25%. Compute the probability of such an event.

- It seems that both in 1994 and 1995, interest rate swings were
particularly large relative to the historical distribution.
Suggest two interpretations for this observation.

** Advanced (1)**

Compute a time-varying volatility of changes in yields using the
RiskMetrics approach to see if the recent volatility is abnormally high.
The exponential model (as used in Riskmetrics) is:

whereVar[dy(t)] = Var[dy(t-1)] * k + [dy(t-1)*dy(t-1)]*(1-k)

Compute the monthly volatility forecast (the square root of Var[dy(t)]) and discuss whether recent interest rates swings are explained by elevated volatility.

** Advanced (2)**

Next, we check whether the assumption of a
conditional normal distribution seems adequate for changes in yields.
Compute the number of exceptions at the 1-tailed 95% level, using the
monthly volatility forecast just computed and the actual increase in
yield.
Test whether the number of exceptions is in line with what was expected.

(For the exception test,
you can use the normal approximation to the binomial distribution.
Also, be careful to match the volatility forecast with the subsequent
change in yield.)

** Really Advanced (Optional)**

The historical simulation approach assumes that changes in
monthly yields have an independent, identical distribution (i.i.d.)
The issue is whether this assumption is appropriate:

- Consider now a model with mean-reversion in the mean, such as the
Vasicek model (if seen in the fixed-income course).
Estimate the model, test whether mean reversion seems significant, and
evaluate VAR in the context of this new model.
Does monthly VAR change? What about annual VAR?

- Estimate a GARCH model for the change in yield and compare the
forecasts to that of the EWMA model.

**(4) Hedging.**

- On December 31, 1994, the portfolio manager decides
not to liquidate the portfolio,
but simply to hedge its interest rate exposure.
Develop a strategy for hedging the portfolio,
using (i) interest rate futures, (ii) interest rate swaps,
and (iii) interest rate caps or floors.
For each strategy, describe the instrument and whether you should take a
long or short position.

- On that day, the March T-bond futures contract closed at 99-05.
The contract has notional amount of $100,000.
Its duration duration can be measured by that of the
Cheapest-To-Deliver (CTD) bond, which is assumed to be 9.2 years.
Compute the number of contracts to
buy or sell to hedge the Orange County portfolio.

- This contract has typical trading
volume of 300,000-400,000 contracts daily.
Verify with recent volume data at the
Chicago Board of Trade (CBOT).
Would it have been possible to put a hedge in place in one day?

- Assuming that futures can be sold in the required amount,
would the resulting portfolio be totally riskless?

The county, fortunately, fared much better than had been feared. Disaster was narrowly avoided as schools were paid back just enough to avoid default; the county was able to extend its debt over 20 years. Perhaps the greatest help came from the private sector, in the form of a booming economy leading to greater sales tax receipts and payments by the State.

Since then, the county has filed a recovery plan centered on a $800 million bond issue, in which creditors would be fully repaid. Some county expenses were cut, or transferred to other agencies. Investors in the pool (cities, schools, agencies and the county itself), however, are still facing a $800 million shortfall.

It is unlikely the $1.6 billion loss will ever be recovered.
So far, the county has settled a $2 billion lawsuit against Merrill
Lynch, its principal broker, for $437 million. (Incidentally, this
number is very close to the fall in the market value of Merrill stock
on the day the bankruptcy was announced.)
The county has recovered so far
$650 million, a far cry from the $1.6 billion loss.

Show update on lawsuits

Visit the Merrill Lynch home page and the press release.

The municipal bond market was also badly hit by the bankruptcy. Municipal investments, who were supposed to be guaranteed by the ``full faith and credit'' of the issuer, suddenly appeared vulnerable to default. Munis generally dropped in price relative to Treasuries, which in effect raises the cost of capital for all municipalities around the country.

Additional lessons can be learned from this exercise. Had value at risk been measured before 1994, the Orange County fiasco could very well have been avoided. It is fair to say that, had the Treasurer announced that there was a 5 percent chance of losing more than $1.1 billion over a year, many investors would have thought twice about rushing into the pool. In addition, investors would not have the excuse that they did not know what they were getting into, which would have limited the rash of ensuing lawsuits.

John Moorlach, the new Treasurer until 2006, has instituted new investment policies for the investment pool. Thereafter, Moorlach was elected to the Board of Supervisors.

Visit the Orange County home page

Read the full account of the Orange County disaster,

Big Bets Gone Bad:
Derivatives and Bankruptcy in Orange County,

published by Academic Press (September 1995).

In response to billion-dollar losses (Orange County, Barings,
Daiwa, Metallgesellschaft...), the financial industry is turning to
Value at Risk (VAR) as a method to control market risks.

Professor Jorion wrote the first book on VAR

Value at Risk: The New Benchmark for Controlling Market Risk,

published by Irwin Professional (July 1996).
The book has been translated into Chinese, Hungarian, Japanese, Korean, Polish,
Portuguese, and Spanish.
It has been called an "industry standard".

A new edition was published in 2006.

To learn more about risk management, read the
Financial Risk Manager (FRM) Handbook.
This is the official book for the FRM examination organized by the
Global Association of Risk Professionals (GARP).
This Handbook provides the core body of knowledge for financial risk
managers.

A new edition was published by Wiley in 2010.

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This case was prepared as a basis for class discussion rather to

illustrate effective or ineffective management practices.