Endowment Management MS&E 348 Final Project March 10, 2011 - PowerPoint PPT Presentation

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 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

A Primer on the Stanford Endowment $20 Fifth largest endowment in the U.S.  18 17.5 31% of Stanford’s operating budget funded by payouts  $18 Seeks payout of 5.5% of beginning-of-year market value  $16 15.2 using a 70/30 split of current year performance and target rate 13.8 13.7 $14 12.6 Even split between fully-restricted, unrestricted, and  11.4 partially restricted (Trustee approval) $12 11.3 10.2 10.1 6,500 assets / funds  $10 9.2 8.1 $8 6.3 6.3 $6 5.3 3.7 3.5 3.7 3.8 4.3 4.5 4.6 $4 $2 $0 Source: GAO report on Endowments (Feb. 2010)

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

Data Sources & Assumptions Data Sources / Comments Asset class #1: Equities • Yahoo Finance for net returns (assumes dividend Two options: U.S. (S&P 500) or Asian (Hang reinvestment) Seng index) • Monthly returns Jan. 1994 – Jan. 2011 (n=206) Asset class #2: Bonds • Yahoo Finance for net returns (assumes dividend Three options: U.S. treasuries (Citi 10-year reinvestment) Treasury Index), U.S. investment grade bonds • Monthly returns Jan. 1994 – Jan. 2011 (n=206) (Barclays Aggregate Index), U.S high-yield bonds (ML High Yield Master II Index) Asset class #3: Alternative Investments • Long/Short Hedge Fund index from Dow Jones Credit One option: Hedge funds 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 • Interview with Stanford endowment manager Estimated as 5% of wealth • 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

Model Specification  Decision Variables x it  amount of asset i owned in time period t y it  amount of asset i sold in time period t z it  amount of asset i bought in time period t  Objective Function    Z  E [ U [ W 15 ]]  1 Max U [ W 15 ]   5  10  15 where W15 = “terminal” wealth = Σ x i,15 – liquidation costs – terminal payout, and U[X] is a [piecewise linear function]  Constraints Rebalancing constraint ( μ =trans. cost of selling > 1.0, ν =trans. cost of buying < 1.0, f = payout percentage): x it  x it  1   y it   z it  fx t  1  x it  x it  1   y it   z it  fx t  1  0 All variables are non-negative

Indexed Return (1 = Dec. 1993) 0 1 2 3 4 5 6 Dec-89 Historical Returns by Asset Class May-90 Oct-90 Risk-free (Cash) U.S. Investment Grade Bonds (Bond 2) U.S. Equities (Stock 1) 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 U.S. High-Yield Bonds (Bond 3) Asian Equities (Stock 2) 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 Long/Short Hedge Fund (Alt Inv) U.S. Treasuries (Bond 1) 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

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 20 3 = 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

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

Initial Rebalancing  Intuition: if W is “on target” toward terminal wealth, then asset allocation should shift towards bonds

Subsequent Rebalancing  Demonstrates scenarios where there is no need for equities

Final Rebalancing  “Jaggedness” due to multiple optimal solutions?

Distribution of Terminal Wealth  Mean = 3.99  % of scenarios less than 1.03^15 (i.e. capital preservation + inflation) = 4.0%

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%

In-period simulation 1994 1999-2003 1994-1998 2003-2008 57% 45% 14% Equities Equities Equities Equities 13% 25% 56% Bonds Bonds Bonds Bonds Cash = $1.0 30% 30% 30% Cash Alt. Inv Alt. Inv Alt. Inv Alt Inv. 0% 0% 0% Cash Cash Cash Cash Payout Payout Payout T = 10 T = 0 T = 0 T = 5 T = 15 T = 15 $1.84 $2.38 $2.74 (13% CAGR) (5% CAGR) (3% CAGR)

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

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

Additional Model Extensions  Inclusion of constraints on portfolio turnover  State-dependent endowment payouts  Inclusion of donations (i.e. positive cash inflows)  Alternate utility functions