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Functionality of Banks and Hedge Funds and C ontagion
Between Financial Institutions
Andrew Lo
Harris & Harris Group Professor
Sloan School of Management
50 Memorial Drive, Bld E52, Room 432
Cambridge, MA 02142-1347
Phone: 617-253-0920
Fax: 781-863-9695
alo@mit.edu
Mila Getmansky
PhD Student
Sloan School of Management
30 Wadsworth Street, Bld E53, Room 358
Cambridge, MA 02139
Phone: 617-253-8094
Fax: 617-468-8132
mgetman@ mit.edu
ABSTRACT
The paper studies crises and contagion effects in the framework of two financial
institutions: a bank and a hedge fund. System dynamics models of a hedge fund and a
bank are formulated. The concept of contagion is discussed in the framework of these
two financial institutions. The goal of the paper is to understand conditions under which
each of the financial institutions can fail and determine when a failure in one financial
institution can trigger a contagion effect that leads to the failure in another financial
institution. Both models and the concept of contagion are validated and discussed within
established financial frameworks. The paper provides conclusions and policies how to
avoid or mitigate the effects of financial crises and contagion.
INTRODUCTION
Section 1 gives an overview of the general structure of hedge funds and banks as
well as background for these financial institutions. Section 2 provides a framework for a
generic model. A generic model is made to account for both bank and hedge fund
structure. Appendix A provides equations for the running model. Section 3 along with
Appendix B provides the reasons behind financial crises in each of the financial
institutions. The issues of contagion between a bank and a hedge fund are discussed in
Section 4. Section 5 explains how validation and calibration of the model should be
done. Recommendations and conclusion follow.
The goal of the paper is to understand conditions under which each of the
financial institutions can fail and determine when a failure in one financial institution can
trigger a contagion effect that leads to the failure in another financial institution.
Section 1
Hedge Funds
Since 1990s there has been a growing awareness about hedge funds. Hedge funds
are often called altemative investments because hedge fund managers are not restricted to
any particular type of investments. Hedge funds have the ability to buy (long) or sell
(short) securities that they do not hold. They are not restricted to plain "buy and hold"
strategy. Hedge funds' activities are usually not transparent to investors and to the
government. Hedge funds have the capability of leveraging - borrowing against their
existing assets. In 1990 there were about 70 hedge funds. There are about 50,000 hedge
funds in 2000. The hedge funds also grew in size of assets under management.
Currently, there are about $8 to $15 trillion dollars invested in these alternative
investments. Despite spectacular growth and performance in double digits of various
hedge funds, there have been many horrifying collapses and bankruptcies of hedge funds
such as Granite Capital, Global Systems fund, and LTCM.
The current form of most U.S. hedge funds is a limited partnership, or a limited
liability company established to invest in public securities. However, there is no
common definition of a hedge fund. Hedge funds are defined by their freedom from
regulatory controls stipulated by the Investment Company Act of 1940. The controls
limit fund leverage, short selling, holding shares of other investment companies, and
holding more than 10% of the shares of any single company. However, the laws are
relatively lax, especially compared to the laws that mutual funds have to abide by. Like
mutual funds, hedge funds are actively managed investment portfolios holding positions
in publicly traded securities. However, unlike mutual funds, hedge funds have a bigger
flexibility in the kind of securities they can invest. Hedge funds can invest in domestic
and international debt and derivative securities. They can take undiversified positions,
sell short, and level up the portfolio.
Hedge funds seek to generate above-average retums to their investors. Most hedge
funds use the following strategies:
¢ Short selling. The strategy involves the sales of borrowed securities hoping the price
of these securities will go down. A hedge fund manager should have sufficient skills
and expertise to identify overvalued securities and being able to cost-efficiently
borrow the overpriced stocks.
¢ Hedging. The strategy involves decreasing risk inherent in hedge fund's portfolio.
The risks might be the following: political, economic, company, interest rate and
market risks. Hedging can use the combination of derivatives and short sales. Hedge
fund managers should be able to use efficient hedging techniques. For example, it is
very costly and not efficient to hedge by shorting a share of a stock for every share
held long in the portfolio. It might be more economical to short contracts or shares of
different assets which are highly correlated with the underlying asset.
« Arbitrage. The strategy involves finding any price inefficiencies or discrepancies
between securities or markets. The strategy is risk-free; however, in current efficient
markets it is very hard to find any price inefficiencies. Even if such inefficiencies are
found, they do not last. Therefore, fund managers tend to use leverage in order to
enhance retums due to such minuscule short-term opportunities.
¢ Leveraging. The strategy involves either borrowing money, to increase the size of the
portfolio; or assigning cash or securities as down payment, collateral, or margin fora
percentage of the position one seeks to establish.
¢ Synthetic positions or derivatives. The strategy involves using derivative contracts to
establish certain positions or strategies in the hedge fund.
There are many hedge fund types. The list of hedge fund types is the following:
* Macro funds
¢ Special-situation funds
¢ Pure equity funds
* Convertible arbitrage funds
¢ Funds of funds
¢ Market-neutral funds
¢ Commodity trading advisor funds
¢ Private equity funds
¢ Risk arbitrage funds
¢ Long or short funds
¢ Emerging market funds
¢ Event risk funds
¢ Restructured or defaulted security funds
The structure of a typical hedge fund is provided below. Hedge funds increase
capital by borrowing from wealthy investors, taking loans from the bank and reinvesting
net retum on investments. The diagram below describes both material as well as
information flows. For example, capital can only be increased or decreased by material
flows. However, performance fees can be adjusted to past performance fees, track
performance, the effort exerted by managers, managers’ skill and other parameters.
Investment performance depends both on assets invested as well as on the skill of hedge
fund managers.
Hedge Fund - Functional Diagram
| Limited partnership
Cash inflow
Cost,
= inflow
(ea ~ ~~ _
oe ] Trading
Global _-~"|_ incentives
interest rates wae es
7 Managers”
Strategy abilities and
2 a information
Lack of / *
[transparency | / Cashlinvested x
Lack of
regulations
Banks
Banks have been in the USA since the 19 century. They are structured to
promote depositor safety and economic stability. Federal Reserve is supposed to make
emergency loans to commercial banks. Banks by law have to keep 10 % reserve
requirement. They cannot invest all of their money like hedge funds. Banks primarily
make money by taking deposits and lending money as loans. Interest rates charged on
loans are much greater than the ones promised to depositors. However, banks can also
invest some part of their assets into more risky assets. Banks are financial institutions
whose main purposes are the storing and lending of money. Banks, like most large
companies, are owned by stock holders. These stock holders elect the individuals who
run the operations of the bank, the board of directors. The stock holders also reap the
benefits of the profits that the bank makes. Banks make it desirable for customers to
store their money thereby offering both security and also profit for the customer in the
form of interest on deposits. The security inherent in a large financial institution is
enhanced by federal protection of the depositers’ funds, in the form of the Federal
Deposit Insurance Corporation (FDIC). A bank invests the money it holds, reaping profit
on the earnings from these investments. Another service offered by banks is the lending
of money to individuals and institutions. Customers take advantage of these loans for
things ranging from mortgages to car purchases to business expansions. These loans are
repaid to the bank with interest, and it is on this interest that the bank makes a significant
portion of its profit.
The net profit made by a bank is a balance between the profit due to the returns on
investments and the interest paid to the bank on loans and the expenses due to the
operating costs (salaries, buildings, etc.) and the interest paid to customers on their
deposits. A bank will often delve into other areas of financial business. Many banks
offer credit cards, mutual funds, insurance and currency exchange. Banks occupy a very
important niche in the economy. When a bank lends money it allows a business or an
individual to borrow against their future income in order to accomplish things they
otherwise couldn’t. Further, it allows businesses and individuals to store, and make profit
on, their wealth with minimal risk.
A simple diagram based on banks’ functionality is drawn below.
Functional Diagram of a Bank
interest payments
interest
besseeel® on loans
on deposits deposits lending
withdrawals SE 7
PSs oeenight loan repayment
returns on “oer
investments
Section 2
Research Question
The proposal is to study the ways a generic hedge fund can fail. Under which
conditions a generic hedge fund might fail? It is imperative to find the leverage points in
the hedge fund's structure and decision points which lead to the collapse of the generic
hedge fund. (Note, as was mentioned in the introduction, we are building a model of a
generic financial institution, and then calibrate it to a specific one. For this paper, a
model was calibrated to a hedge fund. That’s why we will often make references to a
model of a hedge fund.)
Method
In finance, the following saying that is true - the past does not guarantee the
future. If a hedge fund failed due to one cause, it does not mean that other hedge funds
will fail only due to this cause. It is true that a huge leverage of LTCM in 1998 was the
main factor which led to the almost bankruptcy of the fund. Other hedge funds that had
similar structure as LTCM had to go down. However, other factors should be included in
the equation in order to predict the possibility of a hedge fund to go down. In order to
address the problem of hedge fund failures, it is imperative to study a generic hedge fund
structure thoroughly. It is important to identify all stocks and flows which are the
backbone of an operational hedge fund. After this is done, major effects which lead to
the change in flows should be identified and measured. To illustrate, a fund's value is
called the net asset value (NAV). NAV is going to be a dependent variable. NAV is the
sum of cash, total investments less liabilities.
NAV =Cash + Total Investments - Liabilities
NAV isa function of hedge fund's leverage, reputation, retum, risk of positions,
skill and other factors. Of course, there are many more variables that affect NAV.
However, it seems that leverage, return, risk of positions and skill are the most important
to study. They vary a lot with NAV and they are the answer why hedge funds can fail.
The skill of managers is a huge factor that determines NAV. A skillful manager can
deliver above average returns; therefore, increasing NAV of the fund. New investors,
who are aware of the skillful manager, are eager to invest with this manager. Leverage is
one of the defining elements of a hedge fund's operations. It is an important component
which affects returns and the additional benefits or value added they bring to investors.
By allowing managers to increase the size of the hedge fund portfolio due to leverage,
hedge fund managers are able to magnify their returns. Since many hedge fund managers
are paid on the basis of performance, the greater the leverage, the greater the fund's
potential returns and performance fees. Leverage is an important factor for the study of
hedge funds collapse. Overleveraging to boost fees is a common temptation faced by
many hedge funds. Excessive leverage is the major cause of hedge fund losses in volatile
or falling markets. For example, LTCM collapsed in the summer of 1998 due to the use
of high leverage ratio which magnified relatively minor but unexpected negative price
moves during that time. Risk of positions is an important factor in looking at NAV.
Investors tend to stay away from risky funds which have high volatility stocks with
negative returns. However, they are more eager to invest with funds which have risky
positions in instruments which bring positive retums. Retum of a fund is of course, an
important variable. Investors will fly away from funds which consistently bring negative
returns or less than expected returns (compared to their peers or to the indices).
We are interested in finding the exact dependence of NAV on the independent
variables. Therefore, the problem is to find "f", where
NAV = f(leverage, retum, risk of positions, skill) + E
The equation below is wrong and oversimplified. NAV is not linearly dependent on the
following factors. Hedge fund operations has many implicit feedback loops which do not
lead to a simple linear dependence. The model in the following section is going to fully
address needed feedback loops.
NAV =b1 * leverage + b2* retum + b3 * risk of positions + b4*skill +E
Where b1..b4 are regressors of NAV on leverage, return, risk of positions, and skill
respectively. E =is the error.
Estimation of Variables and Problems in Finding Data
It is very hard to find data on all independent and even dependent variables. The
hedge fund industry lacks transparency. Hedge funds are heavily dependent on
intermediaries devoted to matching buyers and sellers who have every reason to limit the
flow of information to the public. These intermediaries charge substantial commissions
for their efforts, and are eager to limit the distribution of information to investors in order
to maintain their roles. Fund managers are also interested in maintaining the lack of
transparency because they are engaged in arbitrage strategy and are not interested in
revealing positions or order flows. However, with the growth of hedge funds, recent
collapses of huge hedge funds and the push from international regulators, a growing
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number of publications and sources now offer hedge fund data. Laws are also changing.
For examples, the U.S. Securities and Exchange Commission ruled in 1997 that hedge
funds could distribute data using an Internet subscriber service, provided only "qualified
investors" have access to this information.
A hedge fund's prospectus contains information on the fund's investment strategy,
philosophy, as well as its track record. Track record of the fund is another important
source. A hedge fund track record is simply the historical presentation of the fund's
historical returns as measured by the changes in its value over time. The track record
tells how NAV has changed over time.
NAV
It is important to realize that NAV (dependent variable) which is quoted in the track
record might have errors associated with it. The sources of such errors are the following:
¢ The Relevance Problem. Some funds present pro forma returns - theoretical returns
what the fund could have made in the past had such a methodology, manager, or asset
composition been used. Pro forma statements are particularly commonly used by
funds of funds, new hedge funds and system-following commodity trading advisers.
In general, since these retums have not been validated by actual market events, pro
forma track records should not be considered in evaluating NAVs.
¢ The Consistency Problem. Usually, the longer we have retums for a manager, the
better and more precise is our evaluation of the manager and his fund. However, the
longer we have returns for a manager, the higher is the probability that the manager
uses other managers to run the fund or he combined several funds into one fund. The
data should be adjusted for the radical change in strategy, markets, leverage and any
change in management structure in order to evaluate the correct NAVs.
¢ Fees. All fees should be subtracted from overall earnings in order to get consistent
estimates of NAVs.
¢ Valuations. NAV requires that the assets and liabilities of a fund be valued at a
prevailing market price. However, there are different techniques for calculating
NAVs which are reported in funds' track records. The prevailing techniques are the
11
following: marked to spot, marked to model, and marked to market. Marked to
market should be always used.
Risk of Positions
Generally, the higher a fund's standard deviation, the greater its risk for an
investor. Standard deviation of the fund is going to be used as a metric for measuring the
risk of the fund's positions. However, it should be noted that the standard deviation of
the fund's returns is not perfectly correlated with the general risk of the fund for an
investor. The correlation coefficient is 1 only when retums are normally distributed. If
retums are nomally distributed, thus symmetrical, ranking funds by means of average
retums and standard deviation will give meaningful results. However, if returns of the
fund are skewed, then results should be adjusted. The presence of skews means that it is
imperative to distinguish between positive and negative standard deviations and
volatility. Real-world investors are more sensitive to losses than to gains. They prefer
positive volatility (positive retums greater than the fund's average returns). Investors
seek to avoid negative volatility (negative returns greater than the fund's average returns).
Therefore, all other things being equal, a fund with high positive volatility will always be
more attractive to an average investor. (Prospect Theory). It is important to adjust for
the skews because in reality the assumption of normality in the distribution of hedge fund
retums is generally incorrect.
Returns
It is incorrect to assume a normal distribution of returns for a typical hedge fund.
In a simulation model where sometimes returms are deterministically or stochastically
used as an input to the model in order to test the effect of retums on NAV, it is imperative
to make the correct assumptions about retums. For example, most hedge funds have the
loss "tail" in the distribution of returns. It is more frequent than should have been
predicted by a normal distribution. Also, all the distributions have a positive skew; that
is, the frequency of positive returns is to some degree greater than should have been the
case under the normal distribution. Positive skews might be explained by the skills of
12
hedge fund managers. Hedge fund managers charge enormous fees and higher the best
people in the industry in order to deliver better than average positive retums. Therefore,
the more skillful the managers, the less likely their returns will be to conform to a normal
distribution. These skillful managers tend to hold on to assets with positive volatility and
sell assets with negative volatility. Hedge funds' retums can be found in investment track
records of hedge funds.
Skill
Manager's skill depends on prowess and risk management strategy. Prowess is
the ability to identify and capitalize on situations that have high reward and lower risk
than perceived by the market. Risk management is the manager's ability to cut losses and
let winners run. In a way, a good hedge fund manager has a linear utility function
compared to average investors who have convex utility functions when faced with losses,
and concave utility functions when faced with the possibility of future gains. A skill is
usually hard to measure since this variable is often dependent on many other factors. It is
also dynamic in nature. A hedge fund manager's skill can be decreased or increased over
the life span of the fund. The following metric is proposed for the estimation of the
hedge fund manager's skill. It is called D ratio.
D ratio = Abs D/U, where
D=number of positive returns
U=number of negative retums
Abs = absolute value
The D ratio will have a value between 0 and infinity. A D ratio of 0 is a distribution of
retums that have no downside. A D ratio of 1 is a perfectly equal distribution of returns
around 0. A D ratio of infinity signals that managers have a low skill and cannot deliver
any positive returns to their investors.
13
Leverage
Leverage is the value of assets or positions a fund has over and above its capital.
The larger the market value of a fund's positions over its investor supplied capital, the
greater the fund's leverage. The following statistic can be used to calculate leverage:
Leverage = (Total Investments)/ (Total Investments - Liabilities)
Another proxy is a Debt Ratio:
Debt ratio = Liabilities/A ssets
It is important to have the correct leverage ratio in order to make the right assessments of
the impact of leverage on the NAV. Many fund managers do not disclose leverage. Only
one-third of the fund's leverage can be readily determined on the basis of its bank
borrowings. The remainder of the fund's leverage is "hidden" by being contained in the
structured note it is holding in its investment portfolio. Sometimes, only after the
collapse of the fund, the leverage of 50:1 come as a surprise to many of its investors who
did not realize that the manager of the fund used such a high leverage ratio.
Model
There are three important accounting variables that should be represented in the
model: “Assets,” “Liabilities,” and “Equity.” According to the accounting identity:
Assets = Liability + Equity
Each financial institution has three types of assets: “Cash,” “Total Investments,” and
“Loans.” Each of these types of assets is presented as a stock in the final model. These
stocks are the operational stocks of a generic fund. They were inferred from operational
description of hedge funds.
In the model, a financial institution can invest in three types of investments: low-
risk, medium-risk, and high-risk. For example, when a hedge fund invests in a treasury
bond, it invests in a low-risk security; however, when a bank invests in a hedge fund, it
14
invests in a high-risk security. All these relationships are mapped out in the model.
Loans can be short-term or long-term. Note that since we are trying to model a generic
financial institution, the term loans does not apply to all financial institutions, hedge
funds, for example. Hedge funds, by definition, are not able to make loans.
“Cash” can be increased by “Interest Payments,” “Deposits,” “Loan
Repayments,” and “Liquidation of Investments.” It can be decreased by “New
Investments,” “Withdrawals,” and “Lending Rate.” “Total Investments” is increased by
“New Investments” and “Rate of Return on Investments.” However, it is decreased by
“Liquidation of Investments.” “Loans” are increased by “Lending Rate” and are
decreased by “Loan Repayments” and “Defaults.” The variable “Liabilities” has two
additive components: “Increase in Liabilities due to Deposits” and “Interest Owed to
Depositors.” “Liabilities” is decreased by the rate “ Decrease in Liabilities due to
Withdrawals.” Finally, “Equity” is increased by “Capital Gains” and “Increase in Equity
due to Interest Payments.” “Equity” is decreased by “Decrease in Equity due to Interest
Owed to Depositors” and “Decrease in Equity due to Defaults.” Negative equity stock
means that a financial institution failed.
The diagram below shows a stock and flow structure of a generic financial
institution.
15
B
Interest payments
v Deposits: a [ Tner. in L. due to v
Deposits.
: Cash Liabilities
Eom RpaTeE >; of Interest owed to
Withdrawals. Decr. in L. due to depositors.
Withdrawals
New investme Liquidation of
investments.
Teal Incr. in E. due to
ny cet Interest payments.
ate of return on
investments.
ow Equity fae
Deer. in E. due to Capital gains
Interest owed to
Lending rate. depositors. cr. in E, due to
7 Defaults.
ans
i
Formulation for the Rate of Return
*Lognormal distribution of returns
Te are continuously compounded single-period returns, IID normal
1
*Single-period gross simple retums Ri are distributed as IID lognormal variates
‘Three types of retums are used: low risk, medium risk and high risk
Rate of Return: Calculation
uty
EIR, J=e4*2 4
Var[R,]=e4 er I]
16
Rate of Return on Investments
. I. is the rate of retum on investments [$/year]
Tit is the total investments [ $ ]
. Ly is the total net losses [ $ ]
Ty “Riliy
Ly =F, at
Section 3
Hypotheses for Collapse of a Hedge Fund
HYPOTHESIS 1: Effect of Leverage on Liquidation, Deposits,
and Withdrawals
The following hypothesis is going to be tested: Hedge funds decide on target
leverage based on their peer group, their own strategy or the current market conditions.
If their current leverage is below the target leverage, they increase their liabilities,
therefore, increasing the cash and total investments of the hedge fund. However, the
combination of the increase in cash, total investments and liabilities leads to the increase
in leverage. Therefore, leverage is increased until the target leverage is reached. This
loop is very important in the study of crises in hedge funds. If hedge funds have a very
high target leverage such as 50:1, they might end up magnifying small decreases in the
market, thus, increasing their exposure to losses. However, if target leverage stays within
the boundary of a sustainable one, then the hedge fund might prevent its collapse. The
diagram below describes the decision of the increase of leverage based on its target
leverage. "B" stands fora balancing loop. It means, that the increase in leverage is
balanced by the target leverage. The leverage will not be increased beyond its target
value. "+" means that an increase in one variable leads to an increase in another. For
17
example, an increase in leverage leads to the increase in the leverage ratio. "-" means
that an increase in one variable leads to a decrease in another. For example, increase in
leverage ratio leads to the decrease in the increase in liabilities.
a a
Total at a Leverage
+
f Levene a
Increase in Liabilities
However, if the balancing loop is absent due to the lack of transparency,
management skill or the lack or reporting, then leverage can grow out of a “normal”
boundary and lead to a collapse of a fund.
HYPOTHESIS 2: Effect of a Rogue Trader on Net Loss
The following hypothesis is being tested: The presence of a rogue trader can
sometimes lead to a financial collapse and contagion. Sumitomo bank (Appendix B)
provides a rich analysis for the reasons of the presence and behavior of a rogue trader in
the bank. Behavior of a rogue trader can be analyzed in the following causal loop
diagram.
Bet
Net Losses» Probability of a
- + Rogue Trader
£
Retum
4
Benchmark Excess
ee __ypbettotmance
R Skill
Matters
As the amount of net losses grows, there is a greater probability of a rogue trader
placing a larger bet. However, the effect of the probability of a rogue trader and the
amount of the bet on retum can be either positive or negative, depending on the skill of
the rogue trader. Skill is reinforced by an increased return eamed by a rogue trader.
Formulation for the rogue trader
lf L t is negative, then rogue trader exists with probability Pitt
“If a rogue trader exists, then
[had =a, /t
100d alt
«Where I pad is a poor investment
[gene is a good investment
a is aggressiveness of a rogue trader
t is time to make a bet
19
Rate of Return: Rogue Trader is Present
“If a rogue trader is present, rate of return on investments is the combination of the
“normal” rate of return and a retum on a rogue trader’ s bet
‘with PUP a rogue trader makes a good bet, and]. it =f. ili ld +19 good
With {—Ppup a rogue trader makes a poor bet, and I. it =I. ile _[ba
The following graph shows simulation of equity of a hedge fund at different
values of aggressiveness of a rogue trader. As can be seen, greater the aggressiveness,
greater the risk the rogue trader takes, and greater is the probability of a total collapse of a
financial institution.
Graph for Equity
600
SS Tare
-3,700
-8,000
0 2 4 6 8 10 12 14 16 18 20
Time (Y ear)
Equity : a=3_1 Dollars
Equity : a=3 Dollars
Equity : a=2 Dollars
Equity : a=1 Dollars
Causes of Banks G oing Under
*No capital gains (capital losses)
-Bank does not make prudent decisions in risky investments
-Market collapses
-Hedge fund makes poor investments
‘Defaults on principal
20
-Hedge fund or another borrower defaults on loans
Defaults on interest payments
Examples:
1. Financing illiquid assets with short-term deposits
2. Expectation about the behavior of other depositors that drives the behavior of any
individual depositor (this causes bank runs)
3. A bank failure can trigger a run on other, solvent banks when bank customers of the
solvent bank assume that the value of banks assets are highly correlated with each
other.
4. Asymmetric information between banks and their depositors.
5. When a bank is in trouble, bank managers and equity holders have an incentive to
gamble for resurrection.
Causes of Hedge Funds G oing Under
«Makes poor investment decisions
«General market conditions are bad
Banks or other lending institutions decide not to lend (make new deposits), especially in
crises times when liquidity is very much needed
The model was simulated under two conditions:
¢ Current run - investing in securities that on average earn positive returns
¢ Poor investments run - investing in securities that on average eam negative
retums
21
Graph for Equity
4,000
2,000
0
0 2 4 6 8 10 12 14 16 18 20
Time (Y ear)
Equity : Current Dollars
Graph for Equity
200
130
Time (Y ear)
Equity : Poor investmentt —______________— Dollars
Section 4
Contagion can arise when two financial institutions are coupled. If a hedge fund
goes down, then it is possible for the disaster to spread itself into a bank, and vice versa.
Of course, contagion only happens under certain structural conditions that are analyzed in
the paper. Every day several hedge funds fail; however, not all banks that lend them
money or invest in them fail. The size of a hedge fund or the percentage of a bank’s total
assets lent to a hedge fund have to reach some critical number (determined by a model) in
order for both coupled financial institutions to fail. The section analyzes such couplings
through which contagion can spread from one financial institution to another.
22
There are two ways for a hedge fund and a bank interact: bank lending to a hedge
fund and investing in a hedge fund. When a bank lends money to a hedge fund, the bank
eams interest on this money. The hedge fund borrows money from the bank to increase
its leverage. It has to pay interest on the money borrowed to a bank. The channel that
describes lending to a hedge fund is depicted below:
Repayment rate
Banks's Hedge edge Fund
SSS ! ———— >}
= Lending rate Fund's Cas! New investments LJavestments
Interest payments
A bank can also invests in a hedge fund. The channel that describes investing in a
hedge fund is shown below. A bank invests in a hedge fund; therefore, it earns interest
on investment. A hedge fund receives money from the bank and usually invests right
away.
Tetum ofa hedge
| Sauce Repayment rate to a bank
y
Tass Tredge edge Finds
Cash Taveseag ina ina Fund's Cash |New investments LJavestments,
hedge fund
Rate of retum on
investments
The following feedbacks between a hedge fund and a bank are modeled.
23
Cost and Risk of Leverage
B2
Risk to
Bank
Cost of Capi
+ Willingness of
Default Risk : Banks to Lend
+ Willingness of HF
to Borrow
R2 Risk
to HF
Leverage Ratio + +
~ M +
oney Lent By
Banks to HF
As leverage ratio increases, the default risk of a hedge fund increases, leading to
an increase in the cost of capital asked by banks. Due to the increase in costs, hedge
funds are less likely to borrow more, thus decreasing the leverage ratio as depicted by B1
loop. However, as the cost of capital increases, banks are willing to lend money at a
higher rate; therefore, the leverage ratio increases as shown by a reinforcing R1 loop. Of
course, the cost explanation is only a half story. The second half is shown by risk. As
default risk of a hedge fund increases, hedge fund managers are willing to borrow more
knowing that if they bring higher returns, then the hedge fund is going to become more
profitable. On a downside, they have nothing to lose - a hedge fund is already ranked as
a fund with a high probability of default. Reinforcing R2 loops depicts this behavior.
Symmetrically, as default risk increases, banks are less willing to lend even if they can
obtain higher retums due to an increased cost of capital. As default risk increases, banks
expect to lose more money by lending to the risky institution. Therefore, they are willing
to lend less. This loop is shown by B2.
24
Return Potential
B2
Risk to
Bank,
Risk Aversion
Cost of Capit
+ Willingness of
Banks to Lend
to Borrow
R2 Risk
= iy to HF ;
Capital Invested By - Leverage Ratio +
Banks in HF ve ~+——_ Money Lent By +
Banks to HF
As was discussed before, banks can also invest in hedge funds. Therefore, as
leverage ratio increases and default risk increases, banks are less willing to invest in a
fund that has a higher probability of getting bust. Therefore, hedge fund equity
decreases, leading to an increase in leverage ratio; hence, a reinforcing behavior depicted
by R3 Risky Leverage loop. Also, as leverage ratio increases, potential return increases,
leading to an increased willingness of banks to invest in the hedge fund. Hence, the
leverage ratio decreases. The behavior is shown by B3 Retum Potential Due to Leverage
balancing loop.
Reputation
25
B2
Risk Aversion Risk to
Bank
Cost of Capit —_
[y* f + Willingness of
Willingness of Banks R3 Risky Default Risk Banks to Lend
to Invest in HF Leverage Hi
+
Capital Invested By
Banks in HF SS
+ Equity +
+ 0 capital invested Banks to'HE
/B4 >
fects of z
ihe ug Gains
a
Reputation’
It is also important to note that reputation is a great factor that should be modeled
in the hedge fund- bank relationships. By law, hedge funds cannot advertise to a public.
Therefore, reputation that leads to the word of mouth effect is essential to have a hedge
fund running. Reputation can be lost by having losses, and can be gained by positive
retums within the hedge fund. As reputation increases, capital invested by banks in a
hedge fund increases. Therefore, equity increases, leading to the decrease in leverage
ratio. However, depending on the effect of leverage ratio on the willingness of banks to
lend (loops B2 and R1), the actual money lent by banks to a hedge fund may decrease or
increase depending on which loop is prevalent at a time. Therefore, it is possible
reputation might be reinforced or balanced depending on different mechanisms.
Section 5
Model Testing
Hypotheses are tested against available data and case studies that have been
collected (Appendix B). Case studies are studies of individual hedge fund and bank
26
collapses. They encompass reasons behind each collapse, the change in NAV in each
case, and the outcome of the crisis. The model is currently being calibrated and checked
for validity.
CONCLUSION
In order to fully understand the ways a typical hedge fund or a bank can fail, it is
not enough to study past case scenarios and find the reasons behind each collapse. Past
case scenarios provide important variables such as manager's skill, return of the hedge
fund, risk of its positions, and leverage. These variables are important decision vehicles
that impact NAV of the fund. One variable or the combination of these variables might
lead to the collapse of the fund. It is imperative to build a model based on the functions
of the hedge fund. Once the model is built, all important decision points should be
incorporated in the model. The interaction of the feedbacks in the system might lead to
potential collapses in individual financial institutions. A good understanding of a model
and contagion mechanism leads to comprehending the reasons behind collapse and
contagion in different cases.
27
APPENDIX A
HEDGE FUND MODEL
Assets=
Cash+SUM(Loans[Types of loans! ])+SUM (Total Investments[Types of
Investments! ])
~ Dollars
“Assets - Liabilities - Equity"=
Assets-Liabilities-Equity
~ Dollars
Average time to repay loans[short term]=
1~-|
Average time to repay loans[long term]=
10*0+1
= Year
Capital gains[Types of Investments]=
Rate of retum on investments[Types of Investments]
~ Dollars/Y ear
"Capital gains."=
SUM(Capital gains[Types of Investments! ])
~ Dollars/Y ear
Liquidation of investments[Types of Investments]=
Total Investments[Types of Investments]* Normal liquidation fraction
~ Dollars/Y ear
"Decr. in E. due to Defaults"[Types of loans]=
Defaults[Types of loans]
~ Dollars/Y ear
"Decr. in E. due to Defaults."=
SUM("Decr. in E. due to Defaults"[Types of loans! ])
~ Dollars/Y ear
"Decr. in E. due to Interest owed to depositors"=
Interest owed to depositors
~ Dollars/Y ear
"Decr. in E. due to Interest owed to depositors."=
"Decr. in E. due to Interest owed to depositors"
~ Dollars/Y ear
New investments[Types of Investments]=
MIN(Cash/TIME STEP,Cash*Weights[Types of Investments]* Normal new
investments fraction\
)
~ Dollars/Y ear
"New investments."[Types of Investments]=
New investments[Types of Investments]
~ Dollars/Y ear
Defaults[Types of loans]=
Loans[Types of loans}*Normal default fraction
~ Dollars/Y ear
28
"Defaults."[Types of loans]=
Defaults[Types of loans]
~ Dollars/Y ear
Normal liquidation fraction=
0.3
~ 1/Y ear
Normal new investments fraction=
0.4
~ 1/Y ear
Rate of return on investments[low risk]=
Total Investments[low risk]* Retums on individual investments[low risk] ~~
Rate of return on investments[medium risk]=
Total Investments[medium risk]* Returns on individual investments[medium risk]
Rate of return on investments[high risk]=
Total Investments[high risk]*Returs on individual investments[high risk]
~ Dollars/Y ear
"Incr. in E. due to Interest payments"[Types of loans]=
Interest payments[Types of loans]
~ Dollars/Y ear
"Incr. in E. due to Interest payments."=
SUM("Incr. in E. due to Interest payments"[Types of loans! ])
~ Dollars/Y ear
"Liquidation of investments."[Types of Investments]=
Liquidation of investments[Types of Investments]
~ Dollars/Y ear
Types of Investments:
low risk, medium risk, high risk
Interest owed to depositors=
Deposits* Interest rate promised to depositors
~ Dollars/Y ear
"Interest owed to depositors."=
Interest owed to depositors
~ Dollars/Y ear
Interest payments[Types of loans]=
Loans[Types of loans]* Interest rate[Types of loans]
~ Dollars/Y ear
"Interest payments."[Types of loans]=
Interest payments[Types of loans]
~ Dollars/Y ear
Interest rate[short term]=
0.2*0+0.1 ~~|
Interest rate[long term]=
0.1
~ 1/Y ear
Interest rate promised to depositors=
29
0.05
~ 1/Y ear
Lending rate[Types of loans]=
MIN(Cash/TIME STEP, Cash*Normal lending fraction[Types of loans])
~ Dollars/Y ear
“Lending rate."[Types of loans]=
Lending rate[Types of loans]
~ Dollars/Y ear
Weights[Types of Investments]=
Total Investments[Types of Investments]/SUM(Total Investments[Types of
Investments! ]\
“Rate of retum on investments."[Types of Investments]=
Rate of retum on investments[Types of Investments]
~ Dollars/Y ear
Returns on individual investments[low risk]=
0.05*0 ~~
Retums on individual investments[medium risk]=
0.12*0 ~~|
Retums on individual investments[high risk]=
0.2*0
~ 1/Y ear
Loan repayments[Types of loans]=
Loans[Types of loans]/A verage time to repay loans[Types of loans]
~ Dollars/Y ear
“Loan repayments."[Types of loans]=
Loan repayments[Types of loans]
~ Dollars/Y ear
Types of loans:
short term, long term
Normal lending fraction[short term]=
0,25/2 ~~
Normal lending fraction[long term]=
0.25/2
~ 1/Y ear
Withdrawals=
DepositstInterest owed to depositors
~ Dollars/Y ear
Normal default fraction=
13.75/13-1
~ 1/Y ear
Cash= INTEG (
"Deposits."-SUM("Lending rate."[Types of loans! ])-SUM("New
investments."[Types of Investments\
!])-"Withdrawals."+SUM ("Loan repayments."[Types of
loans!])+SUM("Interest payments."\
30
[Types of loans! ])+SUM("Liquidation of investments."[Types of
Investments! ]),
50)
~ Dollars
"Decr. in L. due to Withdrawals"=
Withdrawals
~ Dollars/Y ear
"Decr. in L. due to Withdrawals."=
"Decr. in L. due to Withdrawals"
~ Dollars/Y ear
Deposits=
10
~ Dollars/Y ear
"Deposits."=
Deposits
Equity= INTEG (
"Capital gains."+'Incr. in E. due to Interest payments."-"Decr. in E. due to
Defaults."\
-"Decr. in E. due to Interest owed to depositors.",
50+200/3)
~ Dollars
"Incr. in L. due to Deposits"=
Deposits
~ Dollars/Y ear
"Incr. in L. due to Deposits."=
"Incr. in L. due to Deposits"
~ Dollars/Y ear
Liabilities=INTEG (
"Incr. in L. due to Deposits." +'"Interest owed to depositors."-"Decr. in L. due to
Withdrawals."\
13*2/2.2)
~ Dollars
Loans[short term]= INTEG (
“Lending rate."[short term]-"Defaults." [short term]-"Loan repayments."[short
term],
13/2.2) ~~
Loans[long term]= INTEG (
“Lending rate." [long term]-"Defaults."[long term]-"Loan repayments." [long
term],
13/2.2)
~ Dollars
Total Investments[low risk]=INTEG (
"New investments."[low risk]-"Liquidation of investments."[low risk]+"Rate of
return on investments."\
[low risk],
31
200/9) ~~|
Total Investments[medium risk]=INTEG (
"New investments."[medium risk]+"Rate of return on investments."[medium
risk]-"Liquidation of investments."\
[medium risk],
200/9) ~~|
Total Investments[high risk]= INTEG (
“New investments." [high risk]+'Rate of return on investments." [high risk]-
"Liquidation of investments."\
[high risk],
200/9)
~ Dollars
“Withdrawals,"=
Withdrawals
~ Dollars/Y ear
SRC RR RC KR KRG RRR
.Control
SCR CR ROR CR KR CK CK KK KKK RRR
Simulation Control Parameters
FINAL TIME = 100
~ Month
~ The final time for the simulation.
INITIAL TIME =0
~ Month
~ The initial time for the simulation.
SAVEPER =
TIME STEP
~ Month
~ The frequency with which output is stored.
{TIME STEP =1
~ Month
~ The time step for the simulation.
APPENDIX B: TIME LINE DIAGRAM FAILURES: SUMITOMO BANK, BARINGS
BANK, LTCM HEDGE FUND AND TIGER HEDGE FUND
32
SUMITOMO Corp.
External Factors
j=
™ market: high fluctuations & storage costs
+Engaged in future contracts and
in a price-fixing conspiration
+Unauthorized Cu trading
Some Losses ‘| —* Price of Cu fell from the very high $1.3 below $1
L
Cover Up
J
|» Cause: dual position!
— He hid the losses even from mgmt
Bigger Losses = $2. 6 billion in Cu trading losses
q
Reveal Losses
u
Consequences
_—» First the bank reported $1.8 only
then “revised upward”
33
BARINGS
Favorable time to speculate on the Nikkei
External Factors
tillicit trading of the new head clerk
»| at Singapore branch
Some Losses
[— Ist losses: $3 million -- hidden in a secret account:
88888 (deficit balance was reflected as A/R on BS)
J
Cover Up
Cause: dual position! -- he executed trades on
a Singapore exchange and oversaw bookkeeping
of traders at the same time
(trader and monitor of the back room)
4
Bigger Losses
>$250M (end ‘94) TOTAL:
—> + $150M Gan ‘95) + = $73 billion
q
$250M (Feb ‘95)
Reveal Losses
» Left Singapore, flew to Germany where
he turned himself in
q
Consequences
ummmp- BANCRUPTCY
Taken over by ING BANK => ING Barings
34
LTCM
Oniginal Position
(-Short in Treasury bond futures
one on higher yielding (and higher risk)
J
mortgage-backed or corporate bonds
External Causes
Crisis in Russia =>aversion to risk decreased
=>sovereign bond prices increased
a
Some Losses
The speed and extent of that movement
was not anticipated by LTCM
a
More Losses
Causes: arbitraging sovereign debt of G-7
countries and swaps; exposure to emerging,
a
market bonds; the equity derivatives market
Interim Solution
To avoid illiquidity, LTCM tried to raise cash
from commercial banks and sold assets to
u
meet margin calls from its borrowers.
Consequences
Losses: $3.6 billion
Acquisition of LTCM by its creditors
u
Lesson to be learnt
-Avoid excessive confidence in risk mgmt’s
abilities; incomplete information; high
degree of leverage; trading incentives.
35
Tiger Management LLC
Growth rate: -4% in 1998 and -8% in Jan-May
1999 => many clients cancelled their contracts.
Movements of the exchange rates, failure in
investments in the European & American bond
markets, confusion due to Russian crisis.
Dreadful econ. situation in Japan, low interest
rates in the US.
They borrowed from Japan at low interest rates
and tock leveraged positions in the US gov't
securities.
$1.5 billion
The yen went strong, US rates have surged
sharply higher, $ went down, US bond prices
went down.
Tiger was forced to liquidate its positions
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36
