William N. Goetzmann, Yale School of Management, 2000
Roberta Tyler consultants to several university investment offices around the country. She specializes in asset allocation studies. She has accumulated performance figures from a number of different university endowments, as well as information about the typical stocks/bonds/cash mixtures common in the endowment universe. She practices a broad policy approach which means that she makes recommendations about allocations across asset classes, rather than about which managers to chose, or which stocks to pick.
Rivermore College is a small mid-western school with a $130 million endowment as of September 31, 1999. It has long had a fixed investment policy of 50% stocks, 20% Corporate Bonds 20% Government Bonds and 10% cash which has yielded a solid record of performance over the years 1980 through 1999. These are Reported in the table at the end of the document. Rivermore rebalances each year in order to maintain the fixed proportions. This requires, for instance, selling equities when they go up, and buying bonds after a down year. Their equity manager is a successful alumnus of the school who appears frequently on Wall Street Week, and is renowned as a cautious but consistent large-cap stock picker. The bond portfolio is managed by Stanley Morgan Capital, in New York. Most of Rivermore's assets are liquid. Occasionally, real estate donations have been made to the university, particularly in the form of bequests by wealthy alumni. These were generally liquidated in timely fashion, unless the property itself was useful to the college. The university itself is located in a prosperous residential section of town. Most of its buildings are neo-colonial, institutional structures, unsuited for conversion to homes. The university is in an unusual position of having a college art gallery with an extraordinary collection of Abstract Expressionist paintings. A 1999 valuation of the collection for insurance purposes estimated its worth at $200 million.
Enrollment at Rivermore has decreased steadily since its peak of 1550 students in 1995 to a low of 900 in 1999. Thus far, shortfalls in revenues caused by declining tuition have been offset by increased spending from endowment. Since 1980, the annual average spending from endowment has been 4% annually. In 1997 and 1998, the university had to spend 6% and 7%, respectively, and anticipate an additional $10 million for 1999. Contributions to the endowment have continued steadily at 2% per year. Since the role of the endowment has increased dramatically in the past few years, the university has decided to review its past performance and future contributions to the institution.
Howard Weaver is the chairman of the endowment committee for the board of trustees of Rivermore. He found out about Roberta Tyler from a friend of his who serves on the board of Nostradamus University. Nostradamus employed Tyler in 1992 to review the investment policy and to recommend an optimal portfolio mix. Tyler presented an asset mix for the Nostradamus endowment that changed their position in stocks from 50% to 60%, reducing their bond position to 40%. Should Rivermore consider a change in its long-standing investment policy? For that matter, how has the endowment, and its money managers performed over the period since 1980? Weaver decided to have Roberta Tyler and her company look into these issues.
Weaver was also concerned with how risks should be defined in the context of Rivermore's investments. He anticipated the need to continue the spending policy of 5% per year. He felt strongly that 5% represented a "floor" below which the portfolio return should not drop. He wanted Tyler to suggest a policy that minimized the probability of hitting this floor. Last, but not least, Weaver wanted to know whether the board should concern themselves with fundamental questions such as whether the endowment is adequate for the school's future needs. Can they continue their current policy? What if enrollment continues to decline?
In addition to these allocation decisions, Weaver wished to know whether the money managers closely followed the fixed stated objectives of the endowment. He asked Tyler whether there was a way to address this issue.
In preparation for his initial meeting with Tyler, Weaver prepared a list of basic issues he wished her to explore.
1) How well did the Rivermore portfolio perform over the 1980-1999 period? How should performance be measured? Are their managers performing well?
2) What benchmark return should they expect from their portfolio, given their current mix of assets? What benchmark return might they expect for their current level of risk? What is the lowest level of risk they should expect for their current level of historical return?
3) Should they consider changing their policy mix? What time period of estimation should they use as inputs to the optimization process?
4) What would be the long-term expected return of her recommended portfolio? How does this compare to the long term expected return of the current portfolio mix?
5) Use regression analysis to determine whether the historical weights on the asset classes match the policy weights.
When Roberta Tyler and Howard Weaver met, they discussed these basic issues in broad terms. She agreed to present the board with a preliminary report regarding past performance and future policy recommendations.
Assignment:
Prepare Tyler's preliminary report evaluating the policy mix of Rivermore, and succinctly address each of Weaver's questions. Include a preliminary asset mix in your report.
This will require calculating summary statistics and correlations for each series, as well as the use of a mean-variance optimizer. Use safety-first methods to recommend a portfolio that will meet the floor requirement.
Present a forceful argument for using your services, or for focusing on asset policy issues, rather than upon manager choices. Make a few succinct points that might help sway a board member skeptical of asset allocation methods.
A note on importing data to Ibbotson Time Series Editor:
To import Excel File, save as version 4 or earlier, and follow the instructions in Ibbotson Time-Series Editor help. That is, create user defined module to hold the new series'. Then import the series into the new module. The spreadsheet below or the one available for download in the syllabus should have the correct format to do this. The series in the new module should then be available to you to use in your analyzer and optimizer.
S&P 500 TR
U.S. LT Corp TR
U.S. LT Gvt TR
U.S. 30 Day TBill
TR
50-20-20-10
Portfolio
Actual Rivermore
Performance Jan 1980
0.061030
-0.064500
-0.074090
0.007968
0.0035938
0.002949935 Feb 1980
0.003070
-0.066500
-0.046710
0.008858
-0.0202212
-0.008540077 Mar 1980
-0.098660
-0.006200
-0.031460
0.012054
-0.0556566
-0.0725389876 Apr 1980
0.042930
0.137600
0.152347
0.012556
0.08071
0.0556989881 May 1980
0.056210
0.056000
0.041875
0.008095
0.0484895
0.0981000414 Jun 1980
0.029570
0.034100
0.035854
0.006112
0.029387
0.0496345842 Jul 1980
0.067600
-0.042900
-0.047600
0.005281
0.0162281
0.0315016963 Aug 1980
0.013110
-0.044500
-0.043170
0.006388
-0.0103402
0.0300807952 Sep 1980
0.028060
-0.023700
-0.026160
0.007534
0.0048114
-0.0371431355 Oct 1980
0.018650
-0.015900
-0.026290
0.009505
0.0018375
0.0538245415 Nov 1980
0.109530
0.001700
0.010016
0.009570
0.0580652
0.0322813631 Dec 1980
-0.031510
0.024800
0.035152
0.013068
-0.0024578
0.0165279279 Jan 1981
-0.043800
-0.013000
-0.011520
0.010370
-0.025767
-0.0805942593 Feb 1981
0.020800
-0.026900
-0.043550
0.010691
-0.0026209
-0.019527391 Mar 1981
0.038000
0.031100
0.038422
0.012077
0.0341121
0.0940203713 Apr 1981
-0.021300
-0.076900
-0.051750
0.010756
-0.0353044
-0.0186949075 May 1981
0.006200
0.059500
0.062191
0.011544
0.0285926
0.0308218817 Jun 1981
-0.008000
0.002300
-0.017930
0.013475
-0.0057785
0.00011512 Jul 1981
0.000700
-0.037200
-0.035290
0.012398
-0.0129082
0.0350236176 Aug 1981
-0.055400
-0.034500
-0.038590
0.012804
-0.0410376
-0.0578978694 Sep 1981
-0.050200
-0.019900
-0.014490
0.012441
-0.0307339
-0.0450176975 Oct 1981
0.052800
0.052100
0.082901
0.012054
0.0546056
0.10471842173 Nov 1981
0.044100
0.126700
0.141003
0.010676
0.0766582
0.14446976819 Dec 1981
-0.026500
-0.058000
-0.071290
0.008738
-0.0382342
-0.0428517782 Jan 1982
-0.016300
-0.012900
0.004580
0.007958
-0.0090182
0.0342104642 Feb 1982
-0.051200
0.031200
0.018196
0.009238
-0.014797
-0.00178522 Mar 1982
-0.006000
0.030600
0.023094
0.009802
0.008719
-0.0144915815 Apr 1982
0.041400
0.033800
0.037339
0.011292
0.036057
0.0706789768 May 1982
-0.028800
0.024500
0.003402
0.010586
-0.007761
0.0558833163 Jun 1982
-0.017400
-0.046800
-0.022280
0.009573
-0.0215587
-0.028992507 Jul 1982
-0.021500
0.054000
0.050121
0.010507
0.0111249
0.05593656 Aug 1982
0.126700
0.083700
0.078084
0.007623
0.0964691
0.15560633919 Sep 1982
0.011000
0.062300
0.061833
0.005118
0.0308384
-0.0341825402 Oct 1982
0.112600
0.075900
0.063434
0.005901
0.0847569
0.0125210052 Nov 1982
0.043800
0.020100
-0.000200
0.006342
0.0265142
0.0270773526 Dec 1982
0.017300
0.010800
0.031179
0.006738
0.0177196
-0.0239018916 Jan 1983
0.034800
-0.009400
-0.030900
0.006864
0.0100264
0.0265288706 Feb 1983
0.026000
0.042800
0.049165
0.006186
0.0320116
0.0417362809 Mar 1983
0.036500
0.007200
-0.009390
0.006326
0.0184446
0.00579688 Apr 1983
0.075800
0.054800
0.034957
0.007140
0.0565654
0.008579211 May 1983
-0.005200
-0.032400
-0.038580
0.006907
-0.0161053
-0.001165382 Jun 1983
0.038200
-0.004600
0.003904
0.006661
0.0196269
0.008117169 Jul 1983
-0.031300
-0.045500
-0.048640
0.007402
-0.0337378
-0.0306250917 Aug 1983
0.017000
0.005100
0.001997
0.007616
0.010681
-0.0654100706 Sep 1983
0.013600
0.039200
0.050465
0.007607
0.0254937
0.001077844 Oct 1983
-0.013400
-0.002500
-0.013160
0.007611
-0.0090709
-0.0340756018 Nov 1983
0.023300
0.014200
0.018347
0.007035
0.0188629
0.0179671684 Dec 1983
-0.006100
-0.003300
-0.005870
0.007269
-0.0041571
-0.0131908936 Jan 1984
-0.006500
0.027000
0.024357
0.007589
0.0077803
-0.0398323407 Feb 1984
-0.032800
-0.017200
-0.017800
0.007137
-0.0226863
-0.0483960893 Mar 1984
0.017100
-0.023500
-0.015640
0.007280
0.00145
-0.0310762087 Apr 1984
0.006900
-0.007300
-0.010550
0.008139
0.0006939
0.0131087343 May 1984
-0.053400
-0.048300
-0.051610
0.007837
-0.0458983
-0.0999550092 Jun 1984
0.022100
0.019900
0.014972
0.007534
0.0187778
-0.016459931 Jul 1984
-0.014300
0.058600
0.069296
0.008185
0.0192477
0.009405791 Aug 1984
0.112500
0.030700
0.026643
0.008306
0.0685492
0.10268385393 Sep 1984
0.000200
0.031400
0.034250
0.008589
0.0140889
0.0735982469 Oct 1984
0.002600
0.057200
0.056087
0.009957
0.0249531
0.006373036 Nov 1984
-0.010100
0.021200
0.011800
0.007334
0.0022834
-0.0733530455 Dec 1984
0.025300
0.012800
0.009062
0.006426
0.017665
0.003452638 Jan 1985
0.076800
0.032500
0.036401
0.006474
0.0528276
0.0825430771 Feb 1985
0.013700
-0.037300
-0.049290
0.005781
-0.0098899
-0.045880477 Mar 1985
0.001800
0.017900
0.030685
0.006160
0.011233
0.0191653178 Apr 1985
-0.003200
0.029600
0.024232
0.007162
0.0098826
-0.0145163789 May 1985
0.061500
0.082000
0.089571
0.006634
0.0657276
0.0991908935 Jun 1985
0.015900
0.008300
0.014177
0.005546
0.013
0.00061077 Jul 1985
-0.002600
-0.012100
-0.017980
0.006246
-0.0066914
0.0180641972 Aug 1985
-0.006100
0.026000
0.025890
0.005502
0.0078782
0.0154298614 Sep 1985
-0.032100
0.007100
-0.002090
0.006049
-0.0144431
-0.0220213256 Oct 1985
0.044700
0.032900
0.033756
0.006488
0.03633
0.0460595313 Nov 1985
0.071600
0.037000
0.040134
0.006082
0.051835
0.0441096302 Dec 1985
0.046700
0.046900
0.054076
0.006504
0.0441956
0.068386878 Jan 1986
0.004400
0.004500
-0.002530
0.005590
0.003153
0.001324239 Feb 1986
0.076100
0.075200
0.114547
0.005296
0.076529
0.0460131676 Mar 1986
0.055400
0.025600
0.076972
0.005954
0.0488098
0.085489061 Apr 1986
-0.012400
0.001600
-0.007990
0.005208
-0.0069572
-0.0582568608 May 1986
0.054900
-0.016400
-0.050530
0.004934
0.0145574
0.0326726599 Jun 1986
0.016600
0.021800
0.061345
0.005246
0.0254536
0.0543286411 Jul 1986
-0.056900
0.003100
-0.010800
0.005200
-0.02947
-0.058701702 Aug 1986
0.074800
0.027500
0.049927
0.004600
0.0533454
0.0388897426 Sep 1986
-0.082200
-0.011400
-0.050010
0.004500
-0.052932
-0.0414222213 Oct 1986
0.055600
0.018900
0.028894
0.004645
0.0378233
0.0779779973 Nov 1986
0.025600
0.023300
0.026711
0.003904
0.0231926
0.053828281 Dec 1986
-0.026400
0.011700
-0.001750
0.004874
-0.0107226
-0.003588641 Jan 1987
0.134300
0.021600
0.016073
0.004151
0.0750997
0.0337036686 Feb 1987
0.041300
0.005800
0.020179
0.004314
0.0262772
0.093283046 Mar 1987
0.027200
-0.008700
-0.022250
0.004706
0.0078806
0.00875424 Apr 1987
-0.008800
-0.050200
-0.047300
0.004441
-0.0234559
-0.006187499 May 1987
0.010300
-0.005200
-0.010530
0.003760
0.00238
-0.0252086384 Jun 1987
0.049900
0.015500
0.009793
0.004819
0.0304905
0.0529843499 Jul 1987
0.049800
-0.011900
-0.017830
0.004573
0.0194113
0.045279298 Aug 1987
0.038500
-0.007500
-0.016450
0.004711
0.0149311
0.0674747055 Sep 1987
-0.022000
-0.042200
-0.036870
0.004521
-0.0263619
0.00142145 Oct 1987
-0.215200
0.050700
0.062282
0.005973
-0.0844063
-0.0755644507 Nov 1987
-0.081900
0.012500
0.003691
0.003452
-0.0373666
-0.008670662 Dec 1987
0.073800
0.021200
0.016534
0.003914
0.0448382
0.017593185 Jan 1988
0.042700
0.051700
0.066646
0.002942
0.0453134
0.0402862893 Feb 1988
0.047000
0.013800
0.005219
0.004556
0.0277594
0.0352943983 Mar 1988
-0.030200
-0.018800
-0.030670
0.004407
-0.0245533
0.0207578247 Apr 1988
0.010800
-0.014900
-0.015990
0.004616
-0.0003164
0.008170839 May 1988
0.007800
-0.005700
-0.010180
0.005053
0.0012293
0.0240771286 Jun 1988
0.046400
0.037900
0.036842
0.004853
0.0386337
0.0693679035 Jul 1988
-0.004000
-0.011100
-0.016960
0.005072
-0.0071048
-0.0356684321 Aug 1988
-0.033100
0.005400
0.005783
0.005938
-0.0137196
-0.009361236 Sep 1988
0.042400
0.032600
0.034478
0.006167
0.0352323
0.10515568634 Oct 1988
0.027300
0.027300
0.030752
0.006101
0.0258705
-0.001329452 Nov 1988
-0.014200
-0.016900
-0.019630
0.005662
-0.0138398
-0.0738014211 Dec 1988
0.018100
0.003900
0.010969
0.006341
0.0126579
0.041863329 Jan 1989
0.072300
0.020200
0.020327
0.005514
0.0448068
-0.0281150556 Feb 1989
-0.024900
-0.012900
-0.017920
0.006131
-0.0180009
-0.0802058387 Mar 1989
0.023600
0.006400
0.012238
0.006706
0.0161982
0.0319574786 Apr 1989
0.051600
0.021300
0.015896
0.006748
0.033914
0.0795285657 May 1989
0.040200
0.037900
0.040118
0.007873
0.0364909
0.0392384813 Jun 1989
-0.005400
0.039500
0.055017
0.007093
0.0169127
0.0533472599 Jul 1989
0.089800
0.017800
0.023778
0.006955
0.0539111
0.11647909442 Aug 1989
0.019300
-0.016300
-0.025860
0.007392
0.0019572
0.007812725 Sep 1989
-0.003900
0.004000
0.001934
0.006545
-0.0001087
0.005721738 Oct 1989
-0.023300
0.027600
0.037940
0.006765
0.0021345
0.0156637741 Nov 1989
0.020800
0.007000
0.007810
0.006866
0.0140486
0.0317972435 Dec 1989
0.023600
0.000600
-0.000630
0.006069
0.0124009
0.0313898372 Jan 1990
-0.067100
-0.019100
-0.034280
0.005670
-0.043659
-0.0360019975 Feb 1990
0.012900
-0.001200
-0.002470
0.005679
0.0062839
-0.005147208 Mar 1990
0.026300
-0.001100
-0.004380
0.006441
0.0126981
0.048550629 Apr 1990
-0.024700
-0.019100
-0.020200
0.006873
-0.0195227
0.004650844 May 1990
0.097500
0.038500
0.041523
0.006771
0.0654317
0.0576390734 Jun 1990
-0.007000
0.021600
0.023049
0.006251
0.0060549
-0.0337142552 Jul 1990
-0.003200
0.010200
0.010673
0.006771
0.0032517
-0.0176590856 Aug 1990
-0.090300
-0.029200
-0.041850
0.006572
-0.0587028
-0.081168491 Sep 1990
-0.049200
0.009100
0.011683
0.005984
-0.019845
-0.0139324184 Oct 1990
-0.003700
0.013200
0.021524
0.006818
0.0057766
-0.0368838274 Nov 1990
0.064400
0.028500
0.040201
0.005651
0.0465053
0.053602941 Dec 1990
0.027400
0.016700
0.018650
0.005989
0.0213689
0.0527966203 Jan 1991
0.044200
0.015000
0.013035
0.005177
0.0282247
0.0476490447 Feb 1991
0.071600
0.012100
0.003040
0.004767
0.0393047
0.0744016786 Mar 1991
0.023800
0.010800
0.003810
0.004391
0.0152611
0.0641310782 Apr 1991
0.002800
0.013800
0.014029
0.005335
0.0074993
0.0105876111 May 1991
0.042800
0.003900
0.000049
0.004721
0.0226619
0.0322115709 Jun 1991
-0.045700
-0.001800
-0.006320
0.004171
-0.0240569
-0.0305579713 Jul 1991
0.046800
0.016700
0.015745
0.004884
0.0303774
0.0900481918 Aug 1991
0.023500
0.027500
0.034041
0.004610
0.0245192
0.0214443955 Sep 1991
-0.016400
0.027100
0.030345
0.004558
0.0037448
0.006045759 Oct 1991
0.013400
0.004300
0.005438
0.004246
0.0090722
-0.0670620601 Nov 1991
-0.040400
0.010600
0.008199
0.003915
-0.0160487
0.007745915 Dec 1991
0.114300
0.043600
0.058081
0.003792
0.0778654
0.0478169901 Jan 1992
-0.018600
-0.017300
-0.032410
0.003391
-0.0189029
0.0261767305 Feb 1992
0.012800
0.009600
0.005106
0.002828
0.009624
-0.0322905677 Mar 1992
-0.019600
-0.007300
-0.009353
0.003376
-0.012793
-0.006276528 Apr 1992
0.029100
0.001600
0.001589
0.003249
0.0155127
-0.0495794309 May 1992
0.005400
0.025400
0.024259
0.002758
0.0129076
0.0259426859 Jun 1992
-0.014500
0.015600
0.020004
0.003201
0.0001909
0.0224376845 Jul 1992
0.040300
0.030800
0.039778
0.003077
0.0345733
0.0581565638 Aug 1992
-0.020200
0.009000
0.006688
0.002605
-0.0067019
0.0218778431 Sep 1992
0.011500
0.009900
0.018545
0.002573
0.0116963
-0.0288152704 Oct 1992
0.003600
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