Ucla mfe fis_-_2011_02_17_-_pension_fund_quant_-_ash

What does a Quant do in a Pension Fund?

UCLA MFE Financial SeminarFebruary 17, 2011

Arthur Han CFA, FRM, CAIA Global Fixed Income, CalPERS

Disclaimer

Opinions expressed here are solely those of the author’s and do not reflect the opinions of CalPERSdo not reflect the opinions of CalPERS

AgendaAgenda1. Quantitative Portfolio Management2. Analyze Opportunistic Assets3. Build Models for Market Forecasting 4 Cross-Asset Relative Valuation4. Cross-Asset Relative Valuation5. Conclusion

Arthur Han, UCLA MFE Seminar 2/17/2011 3

1. Quantitative Portfolio ManagementQ g• Pension fund investment has a distinct objectives –

matching the liability by investing in suitable asset (ALM)i li bili i f i d h l h b fi f– Pension liability is future retirement and healthcare benefit for

its beneficiaries• Duration of liabilities: 10 -15 yrs

– Capital market is incomplete for ALM managers, because there is no explicit instruments to hedge mortality rate or number of future employees/contributors etc.p y

– The investment focus is long term performance

• As a fixed income quant, my first project was : Develop quantitative portfolio optimization scheme for the long term performance of $1bn corporate bond portfolioperformance of $1bn corporate bond portfolio


Corporate bond: 3 ways to make moneyand 3 excuses to lose them

• Where does a bond portfolio make money?– R = R + R + R– RTotal = RPrice + RPaydown + RCoupon– For corporate bonds, paydown (tender, sinking fund, call, put) return

and coupon return are a.a.s > 0– So one source of possible loss is price returnSo one source of possible loss is price return

• Price return can be broken down risk-parametrically– RPrice = RInterest Rate + RCredit + Rε

Interest rate risk is measure by duration and convexity– Interest rate risk is measure by duration and convexity– Credit risk is measured by OAS and spread duration– Residual ε comes from roll down, trading, extension for hybrids, etc.

Price and ield is in ersel related d e to the “fi ed” str ct re of a– Price and yield is inversely related due to the “fixed” structure of a bond, and are dual of each other


Long term total return of the US Corporate Bond IndexWhat Drives US Corporate Bond Market Return 01/29/2010 314What Drives US Corporate Bond Market Return

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300

01/29/2010, 314

01/29/2010, 314

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150

200

Perc

ent

NUGGETTAG:userName=null&plotName=null

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50

1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010

YearKey Axis Name Last Minimum Maximum Mean SD SD Change

Left Cum. Monthly YTW 318 1 01/31/1973 318 01/31/2011 180 96 0

Left Cum. 1-mo lagged TROR 314 -11 08/31/1973 316 10/30/2009 168 99 2

Source: Barclay’s Capital Live

• Is driven by yield! E[R]= Yield• What is the strategy in light of this simple fact?

Maximize yield while minimizing the price volatility– Maximize yield while minimizing the price volatility– Do this monthly


Is this really a simple problem?C b d P f li• Corporate bond Portfolio– Managed “Top Down” (sector allocation) and “Bottom Up” (Issuer Selection +

Bond Selection)– Yield curve bet is not the PM’s expertise so want to be neutral to the indexp– Thus increase in yield must come from credit spread

• Investment policy has strict limits– 2% max overweight per issuer and 5% max per sub industry

N l– No leverage– No shorting– Composite credit agency rating above BBB-

• Barclay’s Capital US Corporate Index contains over 3,700 bondsy p p ,– Historical data available on monthly basis– How many years of data do you need to estimate the covariance matrix?

• You have 1 billion dollars and likely 200 positions OR LESSB d t d i l t i f 1 illi f (“Di t t”)– Bonds trade in lot size of 1 million face (“Discrete amount”)

– Classic Optimization is requires that “step size” be sufficiently small to not destabilize the iterative algorithm

• Lastly, trading volume per month was constrained to 4% of the portfolio


Simplex junction - what’s your function?S f d t• Source of data– Barclay’s Capital Point: Index information, risk analytics, pricing– Internal portfolio management system

• Risk specification• Risk specification– Credit risk = P[Default]*(Loss Rate) (OR)

= spread duration * spread volatility (OR)= DTS = spread duration * OAS

– Interest rate risk = PV01 (duration, convexity) • Model specification

– Optimized on constrained minimization of DTS with alpha target of 50 bps /yearbps /year

– Closely match duration and convexity (PV01<0.01 bps)– Constraints on concentration, agency rating, negative weight– Shrinkage for covariance matrix estimation (Olivier Ledroit)

M i l i f i i f i di i i– Marginal information ratio for step-wise discretization– Trading cost penalty – “dead zone”

• Output– Monthly trade recommendation reportMonthly trade recommendation report


What happened• DK’ed

– Trader often found that spread from index provider I used for optimization was different from the level available for his execution –an observability probleman observability problem

– Optimizers stubbornly chose illiquid and unavailable bonds, because index data was stale and thus less volatile than it should be – a controllability problem

• Lesson: PM’s heuristics, market convention, uneven opportunity sets and investment policy creates real pp y p yimplementation challenge for a quant analyst!

Next: Stint as a Corporate Bond Trader/Desk QuantOr

Lessons in CynicismLessons in CynicismArthur Han, UCLA MFE Seminar 2/17/2011 9

2. Analyze Opportunistic Assetsy pp• Due to the proliferation of leveraged investors, there were

ample buyers of cash asset and not enough supplyp y g pp y– Because leveraged buyers “arbitraged” funding, asset liability

managers (pension and insurance) who must meet target returns were reaching for yield

• Implicitly and explicitly, ALM managers started to lever up– Markets were orderly – low vol, steady spread, steady returny , y p , y– 130-30, structured products, commodity, private equity, hedge

funds, real estate …..

• Since I doubled as a desk quant, I was commissioned with analyzing the suitability of the structured products to our opportunistic portfolio, benchmarked to high yield index


2H 2005-1H 2007 : Yield Pig Years• Every week I’d get offering memorandum on the slew of credit products• Every week, I d get offering memorandum on the slew of credit products

from US Banks and structured notes from Euro Banks. We had:– Skew products– Dividend swaps– Range accrual– Index TROR– CIPS– Sharpe ratio of hedge fund of fundsSharpe ratio of hedge fund of funds– Catastrophe bond– Mortality linked notes (aka death bond)– KIKO

CDO– CDO– CLO– CLN– CSO2

Picture : Robo-Broker C3PO pitching for“AAA rated principal guaranteed note linked to

– CPDO• Every day, I’d get market quotes from brokers with negative credit basis

package, CDX tranche trading ideas, and cap structure trades (down the quality) Most of them required me to either synthetically generate beta

R2D2 merchandising income”

quality). Most of them required me to either synthetically generate beta (portable alpha) or lever up 15 - 20 times to outperform the index.


2H 2005-1H 2007 : Yield Pig YearsI fid i d id l d i bili f ALL• It was my fiduciary duty to consider value and suitability of ALL the offerings and trading opportunities carefully. So I developed a framework that served me well over years– What is in it for the dealer?What is in it for the dealer?

• Most exotic structured notes are there for Euro Bank’s hedging purposes• Most credit products are there for Agency ratings arbitrage

– Am I getting fair value?• Most principal protected notes can be broken into a derivative and a zero

coupon bond• If I run risk neutral valuation and consider the illiquidity discount, does the

return multiplier or yield I am getting seem fair?Wh i i i f C lPERS?– What is in it for CalPERS?

• How does this product fit in the Opportunistic Portfolio? Does it diversify risk and enhance alpha?

– What are the terms and covenants that can make the deal less risky?y• Key person clause, obligatory provision of weekly liquidity and puttability

criteria


What happened• I was not able to find enough deals that met the criteria, so only 50 million

was committed– Often the work of a desk quant on buy side seems futile, because you may be a

competent analyst and a great gate keeper, and yet you will make no moneycompetent analyst and a great gate keeper, and yet you will make no money – I let out a big sigh of relief for my floors when market crashed in 2008

• Lessons (in cynicism) :– If you can not analyze the source of risk and return, no deal

• Information asymmetry and incomplete market make it hard to value risks that banks were trying to get rid of

– Never take the deal at face value• The catch in the deal is not apparent through quantitative model of the offering

memorandum• Problem 1 : Data used to calculate expected return are too myopic– Need a complete

economic cycleeconomic cycle • Problem 2 : Asset risk return distribution was always assumed normal – In reality, some

asset returns are like short put and some are fat tailed


3. Build Models for Market ForecastingI h l OTC d i i i h ld• Interest rate swaps are the largest OTC derivatives in the world– Notional for interest rate derivatives, which include interest rate swaps and

options and cross-currency swaps was $434 trillion (ISDA Q2 2010) – US Investment grade bond market cap is $17 trillion with duration of 7 yearsg p y

• Pension liability duration is estimated at 10 -15 yrs – Thus for ALM purposes, IR swap overlay should be considered

F f li li i d i IR l h d i– For portfolio replication and interest rate management, IR swap also had merits

• So what was holding us back? – Ambiguity of where the swap spread (Swap yield –Treasury Yield) came fromAmbiguity of where the swap spread (Swap yield Treasury Yield) came from

• Thus we began research and modeling of the swap spreads. Typical modeling involved;– Review of the cross market history– Review of the academic researches– Review of the industry researches– Identifying the relevant variblesIdentifying the relevant varibles– Building “economic” model and “dynamic” model


Market historyHistorical Inter-Markets Spreads

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Y2K Liquidity

Treasury Buyback Announced

GSE's Increase MTG Portfolio.

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Spre

ad

1998 Russia Default- LTCM

1997 Asia Crisis

Monetary Expansion Begins

Mortgage Convexity Hedging

Real Estate & Subprime Debacles. Rate cut begins

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S

S L h LiRegime Change - Vol up due to risk perception and the user base changes

NUGGETTAG:userName=null&plotName=null

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1996 1998 2000 2002 2004 2006 2008

Date

Source: LehmanLive.comg g p p p g

Key Axis Name Last Minimum Maximum Mean SD SD ChangeL ft I t G d B ki OAS 305 151 49 153 02/28/1997 305 151 03/17/2008 97 169 41 155 2 567Left Invest. Grade: Banking - OAS 305.151 49.153 02/28/1997 305.151 03/17/2008 97.169 41.155 2.567

Left U.S. Mortgage Backed Securities - OA 124.198 20.879 01/08/2003 176.711 03/06/2008 57.247 23.496 3.143

Left US Aggregate: Agencies - OAS 86.178 3.626 10/31/1997 91.128 03/10/2008 34.902 12.169 2.149

Left USD SWAP 10Y spread 63.200 30.800 05/19/2003 137.000 05/15/2000 58.623 23.056 1.408


Research review • Academic researchers used variety of econometric methods to describe fundamental

and dynamics of the swap spread• Sell side researches use OLS regression to find tradable variables that can be

presented to clients for tactical trading and forecasting purposespresented to clients for tactical trading and forecasting purposes– Poor out of sample set performance

• Key findings– Treasury convenience yield and repo drives swap spread (Grinblatt, 1995)

• Swap Spread ~ Libor-Repo=(Libor–FF)+(FF-GC)+(GC-Repo)– Swap spread is based on forward LIBOR term structure which reflects the inter-bank

lending default risk (Duffie and Singleton, 1997)– There is credit risk in swap spread based on estimate of collateral (Johannes and p p (

Sundaresan, 2003) – Convexity hedging is a factor from MBS market that markedly affected the swap spread

(Feldhutter and Lando, 2007)– AA corporate bond spread captures credit risk better than LIBOR-GC (same)p p p ( )– Swap spread is driven by yield level and slope, treasury supply and 1mX10yr swaption

vol (Citibank 2006)– Swap spread is driven by rolling 1 yr US budget deficit ,real rate, MBS duration, CDX

and 6Mx10Y swaption vol (JPM 2007)and 6Mx10Y swaption vol (JPM 2007)


List of the variables

Variable Description What is it? Source10yr SwSp 10 year US Swap Spread Risk premium of Bloomberg

receiving fixed vs. floating

1yr Bud Def Rolling 1 year aggregate of budget surplus/deficit A

A measure of near term US Treasury supply

Bloombergbudget surplus/deficit. A positive number is surplus

US Treasury supply

Real Rate 3 month Libor – core CPI (ex food and energy)

Short term funding cost Bloomberg(ex food and energy)

MBS Dur Lehman US MBS Index duration

A measure to monitor hedging need of the mortgage market

Lehman Brothers

g gparticipants

Bank OAS Lehman Credit Index AA 10 yr Bank sub-sector option

A proxy for forward Libor risk term structure

Lehman Brothers

adjusted spread


Why two types of models?• A “fundamental” model attempts to better interpret the data (economics

focused), as opposed to a “dynamic” model that better summarizes data (statistics focused) (Adrian Pagan)

Accounting Structural Linear Regression/Logit VAR VECM ??

Fundamental Dynamic

– For portfolio managers, fundamental model is useful because they have insights into different sectors of the market in light of the economy

• Plus easier to demonstrate explicit linkage and the logic to the board etc.• For longer period forecast – economic data are monthly released

– For traders, dynamic model is better because it is a statistically better fitted model

• He/she wants to know when it is good to enter the tradeg• He/she wants high hit rates – best probability of getting market moves right• Data mostly consist of capital market prices, returns, yields, spreads • Good luck explaining why the AA Corporate spread 8 days before has so much

influence on future swap spread movements to the board! p p


4. Cross Asset Allocation• In January 2009 financial market was still in turmoil• In January 2009, financial market was still in turmoil

– Other than Treasury, almost all markets continued losing value– With so much uncertainty, it was hard to decide where to put the

moneyy• About 1.5 billion dollar contribution came in, and senior managers were in

discussion where to put the money• Based on CPPI, we should put money in the equity, where there were massive

loss past 2 years• Obvious place to consider as alternative was US corporate bond

• We looked at – Three equity indices: S&P500, DJIA, and Russell1000.

Si i di A d BBB d d HY– Six corporate indices: A-rated, BBB-rated, and HY corporate– Three future states of economy: benign, baseline, and deep recession– 5 year time horizon

• D namic relati e al e relationship as markets mo e• Dynamic relative value relationship as markets move– If we assign equal probability to the three states, the ranking order is

USHY > BBB > S&P500 > A > Russell1000 > DJIA• Executed HY trade from April and ramped up• Executed HY trade from April and ramped up


Study methodology• Rating Transition Matrix (1970 to 2003)

A BBB HY Default

A 93.3% 5.8% 0.9% 0.0%

• Empirical Relationship between Default and Recovery Rate

BBB 1.2% 93.4% 5.2% 0.2%

HY 0.1% 2.6% 93.5% 3.8%

• Empirical Relationship between Default and Recovery RateDefault Rates vs. Recovery Rate, 1982 to 2007

70%

30%

40%

50%

60%

e R

ecov

ery

Rat

e

y = 6.3582x2 - 3.9337x + 0.5774R2 = 0.6936

0%

10%

20%

0% 2% 4% 6% 8% 10% 12%

Ave

rage

0% 2% 4% 6% 8% 10% 12%Annual Default Rates


Study methodology

• Empirical Relationship between default and earnings growth

Regression of Default Vs Earnings growth

40%

10%

20%

30%

ext y

ear

y = -3.1576x + 0.2263R2 = 0.3557

-10%

0%0% 2% 4% 6% 8% 10% 12%

Earn

ings

n

-30%

-20%

Default this year


Model Snapshot – Market Prices on 03/23/20091. Equity Index

E it I d DJ I d t i l S&P 500 R ll 1000Automatic Update from Bloomberg

Equity Index DJ Industrial S&P 500 Russell 1000Bloomberg Symbol Indu Index SPX Index RIY IndexDate 3/23/2009 3/23/2009 3/23/2009Current Price 7776 823 447Current EPS 539 67 34Current Dividend 3.62 2.85 2.77Current EPS Multiple 12 07 13 76 14 22Current EPS Multiple 12.07 13.76 14.22

2. Manual Update from Point ReportCredit Index By Rating A (7yr+) A (5-7yr) BBB (7yr+) BB (5-7yr) HY (7yr+) HY (5-7yr)Date 3/23/2009 3/23/2009 3/23/2009 3/23/2009 3/23/2009 3/23/2009Coupon 6.30% 5.22% 6.85% 5.91% 7.91% 8.42%Price 90 92$ 90 10$ 82 43$ 83 99$ 55 78$ 59 59$Price 90.92$ 90.10$ 82.43$ 83.99$ 55.78$ 59.59$

3. Scenario InputBond

Bullish Baseline Deep RecessionRatings Transition Matrix Multiplier 0.90 1.00 1.20 Ann Default Ann Default =Override Recovery Rate =Override , Recovery Rate Ann Average Default for Holding Period 6.76% 7.51% 9.01% , Payout Ratio = Average Recovery Rate 34.05% 31.78% 27.45% , Exit P/E = Holding Period (YR) 5 5 5

EquityBullish Baseline Deep Recessionp

Dividend Payout Ratio 40% 30% 25%OverrideExit Multiple 20 18 11Override

DJ Industrial 11,482 9,180 4,388Estimated Equity Index Exit Price in Year 5

DJ Industrial 11,482 9,180 4,388 S&P 500 1,427 1,141 545 Russell 1000 729 583 279


What happened

• HY portfolio outperformed S&P 500 by 29% by 12/31/2009

– We were able to execute less than half of $1.5 billion• Total US HY market was valued at 700 billion at the time• New ETFs linked to HY index performance also came to market –• New ETFs linked to HY index performance also came to market –

taken large synthetic positions that substituted demands derived from CDX/CDO market

Because there were massive demand for the high yield– Because there were massive demand for the high yield asset, technical probably played into the performance


5. Conclusionh d Q d i i f d?• What does a Quant do in a pension fund?

1. Quantitative Portfolio ManagementQ g2. Analyze Opportunistic Assets3. Build Models for Market Forecasting 4. Cross-Asset Relative Valuation

– He/she takes an active part in the investment process!

• In light of their underfunded status, there are many passionate and earnest inquiries at the pension funds right nownow

– Exciting time to be part of the solution, whether you are on the plan-sponsor side buy side or sell sideplan sponsor side, buy side or sell side


References• Baz, J., D. Mendez-Vives, D. Munves, V. Naik, and J. Peress. 1999. “Dynamics of

Swap Spreads: A Cross-country Study.” Lehman Brothers International Fixed Income Research.

• Collin-Dufresne, P., and B. Solnik. 2001. “On the Term Structure of Default Premiain the Swap and LIBOR Markets ” Journal of Finance 56:1095–1115in the Swap and LIBOR Markets. Journal of Finance 56:1095 1115.

• Duffie, D. and K. Singleton. 1997. “An Econometric Model of the Term Structure of Interest-Rate Swap Yields.” Journal of Finance 52(4):1287–1321.

• Fransolet, L. and M. Langeland. 2001. Understanding and Trading Swap Spreads. JP Morgan.

• Grinblatt, M. 1995. “An Analytic Solution for Interest-Rate Swap Spreads.” Yale University Working Paper.

• He, H. 2000. “Modeling Term Structures of Swap Spreads.” Working Paper, Yale University.

• Johannes M and S Sundaresan 2003 “Pricing Collateralized Swaps ” Working• Johannes, M., and S. Sundaresan. 2003. Pricing Collateralized Swaps. Working Paper, Columbia University.

• Ledoit, O. and Wolf, M. 2004. "Honey, I Shrunk the Sample Covariance Matrix"• Ma, Q., Peng, S., and Schumacher, M. 2006. “Special Topic: The 2006 Citigroup

Interest Rate Swap Spread Model.” Citigroup Global Markets Research.p p g p• Sundaresan, S.M. 1991. “Valuation of Swaps.” In S.J. Khoury, ed., Recent

Developments in International Banking and Finance 5. New York: Elsevier.• Sun, T., S. Sundaresan, and C. Wang. 1993. “Interest Rate Swaps: An Empirical

Investigation.” Journal of Financial Economics 34:77–99.


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