1. Hedge Funds Lecture 2: Risk Management & Portfolio Construction
Zhiwu Chen
Yale School of Management

2. Today’s topics Risk management: easier said than done?
Ways to control risk: pairs trading?
Managing risk with CAPM and APT
Managing hedge fund risk with VaR
Case: Zebra Capital

3. Risk and Return: how much can you take?
$7860
Small stocks
$2279
Large cap
$71
Corporate Bonds
$17
T-bills
Copyright: Ibbotson Associates

4. Copyright: Ibbotson Associates

6. The Meaning of Dynamic Risk: Performance of a 1-Stock Portfolio

7. Performance of a 10-Stock Portfolio

8. Performance of a Diversified 30-Stock Portfolio

9. Diversification and Risk Reduction

10. How do you achieve market-neutrality? Example 1: risk arbitrage
“Pfizer Makes Rival Bid For Warner-Lambert”
Pfizer said it would offer 2.5 Pfizer shares for each share of Warner-Lambert outstanding.
Today’s prices: PFE = $35, WLA = $80
Risk arbitrage: For each 2.5 shares of WLA long, short one share of PFE.

11. Example 2: pairs trading
Long IBM
Short eBay?
Dollar for dollar?

12. Pairs Trading is one type of Statistical “Arbitrage”
Identify a pair of stocks that move in tandem
When they diverge:
short the higher one
buy the lower one
Unwind upon convergence
Give me an example?

13. Who does it? Proprietary trading desks Hedge funds (Long-short)
Morgan Stanley
Nunzio Tartaglia ’s
Other investment banks
Hedge funds (Long-short)
D.E. Shaw?

14. Methodology in the Gatev, Goetzmann and Rouwenhorst (1999) Study
Two stages:
Pairs Formation
Pairs Trading
Committed Capital
full period
when-needed
no extra leverage

15. Pairs Formation Period
Daily CRSP files
Eliminate stocks that missed a day trading in a year
Cumulative total return index for each stock
Also restrict to same broad industry category: Utilities, Transports, Financials, Industrials

16. Trading Period Six-month periods: 1962-1997
starting a new “trader” each month
closing all positions at end of each six month
How many pairs to use? , 20 and 20 after first 100, then all pairs under distance metric

17. Trading Method Open at 2 F (historical F over leading year)
Close upon convergence, or end of six- month period
Same-day vs. wait one day to control bid- ask effect

18. Results for Same Day Trading
Portfolio of 5 and 20 best pairs earn an average of 6% per six month period.
Average size of stocks in pairs: 3rd to 4th decile
Utilities predominate

19. Insert pages here from the paper

20. Example 3: Long-Short Fund
Suppose you want
To buy 100 stocks with low P/E ratios
To short 100 stocks with high P/E ratios, $ for $
What about exposure to systematic and unsystematic risks? How do you match the long and short sides?

21. One solution: apply the CAPM
The risk premium for a stock is a function of its contribution to the risk of the market portfolio
A stock’s risk premium is a function of its covariance with the market portfolio.
E(rn) - rf = rf + n [E(rm) - rf]

22. Under the CAPM Each stock’s return follows:
rn(t) - rf = rf + n [rm (t) - rf] + en(t)
Thus, there is just one source of systematic risk

23. Implications for Market-Neutral Funds
Make the total beta of the Long Portfolio equal the total beta of the Short Portfolio
Show me an example?
Any problems?

24. Or, use the APT factor betas
Multiple factors constitute “systematic risks”, not just the market portfolio!
Show me the equation, please!

25. What factors? Factors include, in addition to market portfolio,
Industrial production growth
Interest rates
Term premium or yield curve slope
Default premium = BBB corporate bond yield - Treasury bond yield
Size factor
Book/market factor
Estimate a beta for each factor using multiple regression

26. Now, how do I make it market-neutral?
You want to make
total factor beta of the Long Portfolio == total factor beta of the Short Portfolio, for every known factor!

27. Problems and Concerns?
How many factors are too few? Let the R-square speak!
But, ultimately, it is difficult to make the Long & the Short sides exactly match.

28. Risk Management
Keep a profile of your portfolio’s exposure to every known risk factor:
Macroeconomic factors: interest rate, inflation, …
Industry factors: oil, retail, semiconductor, ….
Barra, Ibbotson Associates, Northfield . ...

29. Alternative method: use Value-at-Risk (VaR)
VAR is the maximum loss over a target horizon within a confidence interval (or, under normal market conditions)
In other words, if none of the “extreme events” (i.e., low-probability events) occurs, what is my maximum loss over a given time period?

30. VAR: Example
Consider a $100 million portfolio of medium-term bonds. Suppose my confidence interval is 95% (i.e., 95% of possible market events is defined as “normal”.) Then, what is the maximum monthly loss under normal markets over any month?
To answer this question, let’s look at the monthly medium-term bond returns from 1953 to 1995:
Lowest: -6.5% vs Highest: 12%

31. History of Medium Bond Returns

32. Distribution of Medium Bond Returns

33. Calculating VAR at 95% Confidence
At the 95% confidence interval, the lowest monthly return is %. (I.e., there is a 5% chance that the monthly medium bond return is lower than -1.7%)
That is, there are 26 months out of the 516 for which the monthly returns were lower than -1.7%.
VAR = 100 million X 1.7% = $1.7 million (95% of the time, the portfolio’s loss will be no more than $1.7 million!)

34. Monthly Return Distribution with 5 Stocks

35. The Case with 20 Stocks

36. Issues to Ponder on
What horizon is appropriate? A day, a month, or a year?
What confidence level to consider? * Are you risk averse? The more risk averse => (1) the higher confidence level necessary & (2) the lower VAR desired.