From rjaganna@nwu.edu Sat Jul 1 16:30:17 2000 Received: from lulu.it.northwestern.edu (lulu.acns.nwu.edu [129.105.16.54]) by ellen.mpls.frb.fed.us (980427.SGI.8.8.8/970903.SGI.AUTOCF) via SMTP id QAA07197 for ; Sat, 1 Jul 2000 16:30:02 -0500 (CDT) Received: (from mailnull@localhost) by lulu.it.northwestern.edu (8.8.7/8.8.7) id QAA04490; Sat, 1 Jul 2000 16:28:46 -0500 (CDT) Received: from fin18338a (bp194-197.kellogg.nwu.edu [129.105.194.197]) by lulu.acns.nwu.edu via smap (V2.0) id xma004470; Sat, 1 Jul 00 16:27:59 -0500 Message-Id: <4.2.0.58.20000701162720.00bcaef0@lulu.acns.nwu.edu> X-Sender: rja235@lulu.acns.nwu.edu X-Mailer: QUALCOMM Windows Eudora Pro Version 4.2.0.58 Date: Sat, 01 Jul 2000 16:27:48 -0500 To: erm (Ellen R. McGrattan), a-shcherbina@nwu.edu From: Ravi Jagannathan Subject: comments Mime-Version: 1.0 Content-Type: text/plain; charset"iso-8859-1"; format=flowed Content-Transfer-Encoding: quoted-printable Status: RO Ellen Here are some comments. 1. Introduction The introduction, as it reads now makes the following points. Historically equities earned substantially more than bonds This is rather high based on theoretical calculations We look at what risk premium to expect in the future Our conclusion is that in the future, we should expect to get what theory predicts. Why the reader should care does not come out clear. Also, why historical numbers were different from what theory predicts and why the situation has changed going forward has to be explained. You may consider incorporating some motivation. Some suggestions: Asset allocation is of interest to every one. An important input is the expected return on different classes of assets Equities form an important investment class Total value of corporate equities in is $xxx in comparison, investment in housing stock, and consumer durables is xxx dollars; bonds in net positive supply (government and corporate bonds exclude mortgages which are borrowing and lending between individuals and hence nets out to zero in the aggregate is xxxx dollars. Express these numbers in (a) fraction of GNP; (b) $ per household; (c) $ per capita. Also express the balance sheet giving the wealth of an average household. Argue that the fraction invested in equities is large and hence is an important asset class for investment/asset allocation purposes. Historically equities have earned a rather large premium over government bonds. If historically realized risk premium on equities over a rather long period of time is reasonable to expect in the future, then the amount invested in equities should be even larger than what we observe -- use a simple mean-variance optimization framework for illustrative purposes. Hence investors may be expecting less than what history tells us -- or they may be forced not to hold equities due to transactions costs -- and poorer investors may be different from richer investors and may be subject to liquidity constraints (Mankiew, JFE What is a reasonable risk premium given the portfolio holdings of an average household. Mehra and Prescott tried to answer this questions using theory. They came up with the surprising answer that the historically realized risk premium is rather too large to be justified to be viewed as compensation for risk bearing if risk is spread out among the entire population in the USA. They coined the term Equity Premium Puzzle. Hansen and Jagannathan confirmed that the Mehra and Precott conclusion that equities have earned rather too high a premium over bonds to be pure compensation for risk bearing in a perfect market is robust to changes in assumptions regarding investors risk preferences. Mehra and Prescott argue that if investors indeed expected to get what they ex post managed to get on equities, there must be costs to sharing risks through financial markets. They discuss a variety of costs moral hazard, adverse selection etc. Given that information technology has come a long way, transactions costs (including monitoring costs) have come down quite substantially. To the extent risk sharing is easier and transactions costs are less important than before, we should expect future risk premium to be less than in the past. Also, if the risk premium investors demand for investing in stocks has come down, then stock prices would go up hence part of the observed high return on equities in the past may be due to risk premium required for investing in stocks having come down. How do we estimate what would be a reasonable risk premium to expect in the future? We use a simple dividend discount model. If only we know what dividends investors expect to get in the future, we can compute the expected return to holding equities at current level of stock prices. We do not know what investors expect to get. However, we can argue what would be reasonable to expect to get. We find that the reasonable expectations would imply that the expected risk premium going forward is about 1% per year. This is consistent with the premium considered reasonable by Mehra and Prescott. Shiller argues otherwise. he argues that 1% is rather too low. If he is right stocks are over valued and a correction should be expected. Dow36000 authors argue that it should be even less than 1% (zero percent). If they are right, a continued increase in stock prices should be expected. History will tell us who is right. Additional References: Constantinides and Mehra; Heaton and Lucas; Fama and French; Thomas and xxx; Bansal and xxxx; If we are right that going forward the premium is only 1% as in Mehra and Prescott then it has profound implications. Most finance textbooks currently interpret the historical average risk premium of 8% as what one should use in determining the cost of equity capital this view has to change. Even finance professors when asked what they expect to get on equities gave a rather large number. May be Shiller is right the run up in stock prices is not really due to a reduction in required risk premium but asset allocation decisions being determined by plugging in historical average returns for future expected returns. Financial markets may really be having frictionsn there may be costs to transacting in financial markets that may be significant unlike typically assumed in these models that may explain the high historical risk premium. 2. Historical Returns This section is fine. 3. The Puzzle for Historical Returns The title may be changes to What should be the risk premium on equities? Historical risk premium may be misleading history could be very fortunate; or investors were not as able to bear risk or diversify as effectively as they are able to do so now. Hence "now" is closer to the frictionless world theoretical models examine. Both issues play a role. Bring in Figure 7 here arguing that we in the USA are probably very fortunate. If history can not be relied on, can we think of a way to answer the question what should be a reasonable risk premium for equities? Here come Mehra and Prescott. They show how to answer this question right in a perfect frictionless market where there are all kinds of insurance markets for perfectly insuring against all kinds of risk one can think of and where individuals are honest and reveal their intentions truthfully and fulfill their contractual obligations without having to engage in costly litigations. To compensate for bearing the risk associated with risk in equities, Mehra and Prescott estimated that the risk premium should be of the order of 1% to 2% Explain what a utility function is; expected utility; how much risk is there in the aggregate; etc. Introduce another section or subsection on can we reconcile the= Mehra and Prescott estimate of what would be a reasonable risk premium for bearing the risk in equities with the historical high average risk premium? In this section point out the papers on incomplete markets and costly participation in financial markets etc. Mankiew; Rao Aiyagari; Lucas and Heaton; papers on limited stock market participation by xxx; etc papers would be relevant. 4. Estimates for the future Regarding the use of dividend discount model: Point out there are three different portfolio strategies one may consider (a) Buy and hold all the shares that exist at a point in time. Collect all the cash dividends. Do not participate in any repurchase or additional and new issues. This is the same and buying and holding one share. The appropriate dividend is the cash dividend. The price is the current stock price. (b) Buy all shares -- when new shares are issued, do not invest in them. When equities are repurchase, tender your shares. (c) Buy all shares -- when new shares are issued, you pay money to the firms -- when repurchases are done you get money from the firms. All three strategies should lead to the same value for existing equities. However, the constant growth model assumption may be more suitable for cash dividends than for broader measure of dividends implied in (b) and (c). We examine all three -- they give similar answers as to what would be a reasonable value for the equity premium going forward. 5. Conclusions: Rewrite so that it is consistent with the changes suggested to "Introduction". 6. References: Please add the following additional references James Claus and Jacob Thomas, "Measuring the equity premium using earnings forecasts: An international analysis". Using analyst earnings forecast data and the dividend discount model for equity valuation, the authors compute the implied equity premium for six countries. Canada, France, Germany, Japan, UK and the US., for each year between 1985 and 1998. The going forward estimates for each year was around 3 percent or less in each of the six markets. Eugene F. Fama and Kenneth R. French, "The Equity Premium", June 2000. The authors find that the Dividend Discount Model estimates of the equity premium and the historical average coincide for the 1872-1949 period -- about 4%. However, the equity premium going forward has come down steadily to about 1-2% per year -- the same as that estimated by Wadhwani. Hence it may be reasonable to say that the historical equity premium was high and now it is low going forward. John Heaton and Deborah Lucas, "Stock prices and fundamentals" -- NBER Macroeconomics Annual 1999. The authors argue that the increased participation in stock markets can lead to as much as a 2% reduction in the equity risk premium and hence can partially explain the current high level of stock prices. A Simple Model of Capital Market Equilibrium with Incomplete Information", by Robert C. Merton, Journal of Finance, Vol. 42, No. 3. The author considers a world where investors know only about a subset of assets and hence there is incomplete diversification. He shows that the equity risk premium can be substantially higher in such a world when compared to the "perfect capital markets" world considered in theoretical models. Hence there would be substantial benefit to a firm in trying to increase its investor base. This is probably the first paper to discuss incomplete diversification -- an implication is that as and when investor participation in the stock market increases, the equity premium would fall and the stock prices would increase. Ravi Jagannathan Finance Department Kellogg Graduate School of Management Northwestern University Evanston IL 60208-2001 (847)-491-8338 (voice) (847)-491-5719 (fax)