THE EQUITY MARKET RISK PREMIUM OVER 200 YEARS

Prospective Utility and Time-Varying Optimal Asset Allocation……….

CFA Lecture,3rd November,2009,London

Contents…….

• 1.Overview of objectives

• 2.A (very) few words on the ERP

• 3.The Model and associated literature

• 4.Results-UK and beyond…

• 5.Lessons…

1.Objectives tonight

• Briefly review the Equity Market Risk Premium-does it exist,how big is it,how do we explain it?

• Introduce an explanation due to Benartzi-Thaler(QJE,1995) based on tenets of behavioural finance

• Apply these to a long-run of UK data with notably more flexible assumptions

• Ask what can we learn about asset allocation decisions and especially how different macro contexts impact asset allocation

• And what about other(very different) countries?

2.Is there an Equity Risk Premium?

• Since 1926,US stocks returned 7% real pa v 1% for bonds-Benartzi-Thaler,1995

• Siegel-real(US) Equities Bonds 1802-1870 5.7 5.1 1871-1925 6.6 3.1 1926-1990 6.4 0.5…’ERP not a recent phenomena’• Mehra-Prescott suggest investors would need a CRRA of

30 to explain this versus best guesses of 1 in practice• Such an investor would be indifferent between 50/50

gamble between $100,000 and $50,000,and $51,209 for certain

• …other explanations……..eg,Reitz,Constantinides…

Or think investment returns over different periods….

• MaCurdy-Shoven,1992:think a faculty member saving for retirement….

• Over working lifetimes all stock portfolios would have done better than all bond portfolios in ‘’virtually every time period’’

• For 25-year horizons all bond occasionally do better,but always <20% better

• Since 1942 all 25-year portfolios better off all stock-at times 7 fold superior!

• ..investors must be ‘’confused about the relative safety of different investments over long horizons’’(M-S)

More recently a rather different view from the LBS…..

• Country selection bias?US focus….• Avoid survival,success etc biases,1900-2005 for 17

countries….• ERP relative to bills…. Geometric Arithmetic (SD)

World 4.74 6.07(16.7)World(ex-US) 4.23 5.93(19.3) ……relative to bonds….World 4.04 5.15(15)World(ex-US) 4.10 5.18(15.2)

..and what can we learn from 150 textbooks?(P.Fernandez)

• ERP………3-10% pa• 51 books use different premia on different pages(!)• Academics survey in 2000 looking 30 years ahead mean

is 7%,range 2-13%;2001,mean 5.5%,range 0-25%!!!• 4 different concepts identified……. 1.Historical 2.Expected 3. Required 4.Implied………….plea for textbooks to be clear.

Brearley and Myers have ‘’no official position’’(!)

‘’Choose the number you need as bankers do’’

3.One Approach-Myopic Loss Aversion

Benartzi-Thaler(1995)

• Focus on 2 behavioural concepts-loss aversion and mental accounting-and ask,given a historically observed ERP in the US,1926-1990,of 6% pa,(and associated,constant,distribution) along with given loss aversion parameters,what is the implied evaluation period for investors consistent with the (observed) ERP?

• Is this a sensible number?Like once a year?(hint!)• At what evaluation period would investors be indifferent

between all bond and all equity portfolios?Why this??• And what is the optimal allocation between bonds and

equities at this horizon?Does it look like the real world portfolio split…well,yes,fortunately it does…at least of late

Background-psychology of decision making

1.Loss Aversion• -Agents more sensitive to reductions in wealth than to

increases(Kahneman-Tversky,decision making under uncertainty)

• Utility defined over gains/losses relative to some neutral reference point as opposed to wealth as in Expected Utility

• Utility function has kink at the origin,slope of loss function steeper than gain function;ratio is measure of Loss Aversion,often estimated as about 2……

• Some maths………

2.Mental accounting-the implicit methods agents use to code and evaluate financial outcomes,incl investments

• Samuelson(1963)-50/50 win $200,lose $100….accept the gamble?No if play once,yes if 100 times…..

• Consider if the agent had this utility function:

U(x)= x if x> or = 0, =2.5 x if x<0 where x is the change in wealth

….here she would turn down one bet but accept 2 or more as long as she did not have to watch the bet being played out –simple repetitions of the single bet are not attractive if evaluated one at a time

When decision-makers are loss averse they will be more willing to take risks if they evaluate performance/or be evaluated infrequently

• Relevance to ERP………..• The investor chooses between a risky asset paying an

expected 7% with standard deviation 20%,and a safe asset paying 1%(all pa)

• With the same logic as earlier,the attractiveness of the risky asset will depend on the time horizon of the investor

• The longer the investor intends to hold the asset,the more attractive the risky asset appears-as long as the investment is not evaluated frequently

• So both Loss Aversion and a short evaluation period will contribute to an investor’s perceived risk of holding equities………so-called Myopic Loss Aversion

Some relevant literature…

• An experiment in risk taking and evaluation periods,QJE,Gneezy and Potters,1997

• The effect of myopia and loss aversion on risk taking:an experimental test,QJE,Thaler,Tversky,Kahnemann,Schwartz,1997

• Evaluation periods and asset prices in a market setting,JoF,Gneezy,Kapteyn,Potters,April,2003

• Classroom experiments to ‘’support’’ MLA-low frequency evaluation leads to more risk taking and higher prices for risky assets

‘Nudge’-Thaler & Sunstein,2009,Penguin Books

• ……..compare the stockbroker who revalues her portfolio daily,and so feels the pain of daily losses with some regularity,with Mr Van Winkle who,on being told he is about to go to sleep for 20 years and to call his broker to discuss his asset allocation, is indeed very calm and unflustered in the knowledge that over 20 years stocks will almost certainly go up…………

• Many examples of ‘nudges’(or choice architecture) to improve welfare……….’save more tomorrow’

So can Myopic Loss Aversion explain the ERP puzzle?

• Whereas Mehra-Prescott ask how risk averse would the representative investor have to be to explain the observed ERP,B-T ask ,if investors have prospect theory preferences,how often would they have to evaluate their portfolios to explain the ERP?....some math,

• Method of ‘verification’…• Sample from historical(1926-1990) CRSP monthly

returns on stocks,bonds,T-bills• Take 100000 n-month returns,rank from low to

high,compute at 20 intervals along the cumulative distn• Compute PU of these holdings for evaluation periods

starting at 1 month and rising 1 month at a time

Details and interpretation….

• Four different simulations….• T-bills and 5-year bonds• Real and nominal…..B-T focus on stocks v

bonds,nominal• At which horizon are investors indifferent between all

assets in stocks or bonds?..... about 1 year…see figures….how plausible is this…annual reports from brokers,tax filings,etc plus institutional reporting…

• What aspect of Prospect Theory drives results?Loss Aversion-specific form of value function and weighting function not critical,eg,could use actual probabilities or piecewise linear value function…

What mix of stocks and bonds maximises PU at 1 year horizon?And what about ERP v. Evaluation period?

• Compute PU of each portfolio mix at 10% increments

• Max with Stock allocation flat between 30-55%

• Seen as representative of US pensions,endowments…

• Loss aversion may be a fact of life but evaluation frequency is a choice variable…interpretation…actual ERP is 6.5% at an evaluation period of one year,falling to 1.4% at a period of 20 years-’for someone with a 20 year investment horizon,the psychic costs of evaluating the portfolio annually are 5.1% pa’……….

One comparative study-De Groot & Dijkstra(1996)

• de Groot & Dijkstra(1996) replicate B-T for 4 countries,1978-1994…

Evaluation period optimal % in equities (months) at 1 year evaluationGermany 10 50US 3 70UK 5 70Japan 8 45

US figure very different!Sensitivity to data period and series apparent.Evaluation period instability over time in countries……so what about over even longer periods?.....

4.And so to our study,UK,1805-1995

Computational method

• Take Kahnemann-Tversky value function and parameters as before-constancy over long periods??

• Back to K-T ‘dice’ approach calibrated against B-T.• Take fixed and rolling 20-year periods to compute PU for

each evaluation period and then vary asset allocation in 1% increments…..producing the following…

1.PU for 100% bond allocation 2.PU for 100% equity allocation 3.PU and allocation values for optimum asset

allocation We use consols-report here nominal results as B-T. Why 20-year periods?Observe equities>bonds folklore at this horizon.

Optimal Allocation for Non-Overlapping Periods,1816-1995

Relation between PU,evaluation period and asset allocation

Other country optimal allocations,1926-45

5.Comments on results

• ‘’manipulating the evaluation period of prospective clients could be a useful marketing strategy for fund managers’’………’’tying clients’ hands may induce them to evaluate financial outcomes in a more aggregated way’’

• Constant ERP assumption?

• Different countries’ experiences?

• All bond portfolios optimal for low inflation/deflation eras.

• Most recent pre-1995 period,12 month evaluation implies 89% equities for UK-plausible ‘cult of the equity’???

A Final Thought……..

• Do organisations display Myopic Loss Aversion?• Theory is individualistic but most assets held by

institutions• If ‘pension funds have essentially an infinite time

horizon,why not more in stocks?’-MLA,agency costs• Similarly endowments have agency issues plus

spending plan rules……

• And what does recent experience imply for optimal allocations................?