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Endowment Management MS&E 348 Final Project March 10, 2011 Emile Chamoun, Matt Conger, Egill Juliusson Objective Determine an asset allocation for a university endowment under uncertainty Utilize a stochastic optimization model

SLIDE 1

Endowment Management

MS&E 348 Final Project March 10, 2011 Emile Chamoun, Matt Conger, Egill Juliusson

SLIDE 2

Objective

 Determine an asset allocation for a

university endowment under uncertainty

 Utilize a stochastic optimization model

across three time periods, allowing for rebalancing in each time period

 Incorporate transaction costs and payouts

from the endowment

 Objective is to maximize expected utility of

“terminal” wealth, even though endowments are persistent

SLIDE 3

A Primer on the Stanford Endowment

3.7 3.5 3.7 3.8 4.3 4.5 4.6 5.3 6.3 6.3 8.1 11.3 10.1 9.2 10.2 11.4 13.7 15.2 18 17.5 12.6 13.8 $0 $2 $4 $6 $8 $10 $12 $14 $16 $18 $20



Fifth largest endowment in the U.S.



31% of Stanford’s operating budget funded by payouts



Seeks payout of 5.5% of beginning-of-year market value using a 70/30 split of current year performance and target rate



Even split between fully-restricted, unrestricted, and partially restricted (Trustee approval)



6,500 assets / funds Source: GAO report on Endowments (Feb. 2010)

SLIDE 4

Model Schematic

Cash Cash Equities Bonds

Alt. Inv

Cash Equities Bonds

Alt. Inv

Cash Payout Equities Bonds

Alt. Inv

Cash Payout Equities Bonds Alt Inv. Cash Payout Time T = 0 T = 0 T = 5 T = 15 T = 10 T = 15 Deterministic Allocation Stochastic Allocation

SLIDE 5

Data Sources & Assumptions

Data Sources / Comments

Asset class #1: Equities Two options: U.S. (S&P 500) or Asian (Hang Seng index)

Yahoo Finance for net returns (assumes dividend

reinvestment)

Monthly returns Jan. 1994 – Jan. 2011 (n=206)

Asset class #2: Bonds Three options: U.S. treasuries (Citi 10-year Treasury Index), U.S. investment grade bonds (Barclays Aggregate Index), U.S high-yield bonds (ML High Yield Master II Index)

Yahoo Finance for net returns (assumes dividend

reinvestment)

Monthly returns Jan. 1994 – Jan. 2011 (n=206)

Asset class #3: Alternative Investments One option: Hedge funds

Long/Short Hedge Fund index from Dow Jones Credit

Suisse Hedge Fund Index

Net monthly returns Jan. 1994 – Jan. 2011 (n=206)

Asset class #4: Cash

Modeled as inflation-adjusted
Estimated using monthly U.S. consumer price index (CPI)

values Jan. 1994 – Jan. 2011 (n=206) Payouts Estimated as 5% of wealth

Interview with Stanford endowment manager
Association of American Universities “Facts About

College and University Endowments” (Jan. 2009) Transaction Costs

Varies by (1) buying/selling, (2) by asset class, and (3) by

returns in the previous period (i.e., state-dependency)

Interview with Stanford endowment manager

Utility Function

Upside/downside slope methodology

SLIDE 6

Model Specification

 Decision Variables  Objective Function  Constraints

xit  yit  zit 

amount of asset i owned in time period t amount of asset i sold in time period t amount of asset i bought in time period t

Z  E[U[W15]]  1  U[W15]

15



10



 5



Max where W15 = “terminal” wealth = Σxi,15 – liquidation costs – terminal payout, and U[X] is a [piecewise linear function]

xit  xit 1  yit zit  fxt 1  xit  xit1  yit zit  fxt1  0

Rebalancing constraint (μ=trans. cost of selling > 1.0, ν=trans. cost of buying < 1.0, f = payout percentage): All variables are non-negative

SLIDE 7

Historical Returns by Asset Class

1 2 3 4 5 6 Dec-89 May-90 Oct-90 Mar-91 Aug-91 Jan-92 Jun-92 Nov-92 Apr-93 Sep-93 Feb-94 Jul-94 Dec-94 May-95 Oct-95 Mar-96 Aug-96 Jan-97 Jun-97 Nov-97 Apr-98 Sep-98 Feb-99 Jul-99 Dec-99 May-00 Oct-00 Mar-01 Aug-01 Jan-02 Jun-02 Nov-02 Apr-03 Sep-03 Feb-04 Jul-04 Dec-04 May-05 Oct-05 Mar-06 Aug-06 Jan-07 Indexed Return (1 = Dec. 1993) U.S. Equities (Stock 1) Asian Equities (Stock 2) U.S. Treasuries (Bond 1) U.S. Investment Grade Bonds (Bond 2) U.S. High-Yield Bonds (Bond 3) Long/Short Hedge Fund (Alt Inv) Risk-free (Cash)

SLIDE 8

Model Parameters

 Wealth: Initial = 1.0; target wealth = 3.3

Corresponds to a 8% real return over 15 years
In line with historical returns for endowments

 Samples: 20 scenarios for each stage

Implies 203 = 8000 scenarios, with 7 assets * 3 actions

(buy/sell/hold) * 4 stages = 84 decision variables / scenario

672,000 decision variables

 Returns: Pre-sampling  Payouts: 5% of portfolio in current period  Transaction Costs: % of transaction, varies by

asset class and by loss/gain

 Diversification: 30% limit for each asset

SLIDE 9

Initial Allocation

U.S. Equities (Stock 1) 30% Asian Equities (Stock 2) 27% U.S. High- Yield Bonds (Bond 3) 13% Long/Short Hedge Fund (Alt Inv) 30%

SLIDE 10

Initial Rebalancing

 Intuition: if W is “on target” toward terminal wealth,

then asset allocation should shift towards bonds

SLIDE 11

Subsequent Rebalancing

 Demonstrates scenarios where there is no need for

equities

SLIDE 12

Final Rebalancing

 “Jaggedness” due to multiple optimal solutions?

SLIDE 13

Distribution of Terminal Wealth

 Mean = 3.99  % of scenarios less than 1.03^15 (i.e. capital

preservation + inflation) = 4.0%

SLIDE 14

Sensitivity Analysis of Transaction Costs

 No transaction costs: E[W] = 4.02,

% of scenarios with capital loss = 3.5%

 Normal transaction costs: E[W] = 3.99,

% of scenarios with capital loss = 4.0%

 High (10x) transaction costs: E[W] = 3.60,

% of scenarios with capital loss = 5.9%

SLIDE 15

In-period simulation

Cash Cash = $1.0 Equities Bonds

Alt. Inv

Cash Equities Bonds

Alt. Inv

Cash Payout Equities Bonds

Alt. Inv

Cash Payout Equities Bonds Alt Inv. Cash Payout T = 0 T = 0 T = 5 T = 15 T = 10 T = 15

57% 30% 0% 13% 45% 30% 0% 25% 14% 30% 0% 56%

$1.84 (13% CAGR) $2.38 (5% CAGR) $2.74 (3% CAGR) 1994 1999-2003 2003-2008 1994-1998

SLIDE 16

Comparison to Stanford Endowment Performance

$0 $2 $4 $6 $8 $10 $12 $14 $16 $18 $20 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 "Actual" "Simulated"

SLIDE 17

Key Results

 Initial wealth of $1.0 grows to an expected value of

$3.99 after 15 periods, implying a 9.6% annual return

After initial allocation: E[W5] = $1.60 (10% real return),

20% of scenarios have capital loss + inflation

After first rebalancing: E[W10] = $2.56 (10% real return),

2.3% of scenarios have capital loss + inflation

 Initial allocation is 30% to U.S. equities, 27% to Asian

equities, 13% to bonds and 30% to alternative investments

Expected rebalancing after period 1: 30% U.S. equities, 15%

Asian equities, 25% bonds, 30% alternative investments

 4.0% of scenarios demonstrate capital preservation +

inflation through year 15

SLIDE 18