Investments, Thursday May 14, ’09 Today’s 3-part plan Clean-up in Chapter 7. Last year’s re-exam.Last year’s re-exam Chapter 8 and other closing remarks. Many words concepts and thoughts; no cases. And that’s all she wrote

Welfare Gains From Options (?) The trading mechanism matters for equilibrium. (Remember: We got out starnge numbers yesterday.) If option trading is started from ”no options equilibrium”, all are better off. Welfare gain (this alludes to the calculation of expected utilities of all agents.)

Portfolios can change substantially, but not that much in happens in terms of wealth equivalents (= the amounts of extra time-0 consumptions that makes agents equally happy ”before” and ”after”.)

Finance Crashes and F***-ups The remarks are profectic in hindsigt. Companies sell protection for states that bad but not really bad, and ”pick up pennies in front of a steam train”.’ Names: Peso problem, LTCM collapse, financial crisis

Chapter 8: Words & Terms Positive (what people actually do) vs. normative (what people show do) economics. We’ve been ”largely positive”, although the distintics is less than clear. Advisors. (Beware: Salesmen too.) Life-cycle decisions: Education, work, retirement. Pensions: Defined benefit vs. defined contribution. Asymmetric information: Adverse selection and moral hazard.

Chapter 8: Past and future returns Expected returns are hard to predict. Even past ones! Standard deviations are more accurately estmated. The graph on the right is my version of Sharpe’s exepriment in Sec Increasing sampling frequency makes this even more pronounced.

And (Figure 8.4) portfolios based on estimates are all over the place. (The welfare loss, though, is not clear.) Sharpe suggests (Sec ) reverse optimization/engineering: Estimate (co)variances and use (say) CAPM backwards to estimate expected returns. (I’m not sure I 100% understand his experimental design on p )

Correlation caveat W/ 100 companies, there are ~5,000 covariances to estimate. W/ 500 compnies there are more than 50,000 (probably more then the #observations you have). Clearly, simple estimation is unstable. Sol’n: Put some structure on; the single index model, for instance.

May work well for stocks and portfolio choice. And looks very stable. However, correlation is not a suitable measure for dependence in extreme cases. Thus, a ”single index approach” does not work well for credit risk modelling. But that was exactly what people did – under the fancier heading of ”the Gaussian copula model”. The rest is history.

Factor models CAPM type regression of individual stock returns on the market (index) have ”patterns in residuals”. Fama/French say that variations are well explained by to extra factors: ”small minus big” returns and ”growth minus value” returns. Fits right into regression framework. Enourmous literature. (One note: Arbitrage pricing theory in Sec is not what us option people would call it.)

Sec 8.7-8: Investing or Betting? Investing: Take clients’ preferences and positions into account to comprise portfolios. Betting: Try to beat the market based on better predictions. (Picking stocks, strategic asset allocation.) Again, the distinction is fuzzy in reality. Macro consistency is a test: If you advised everybody, would markets clear? If not, you’re betting.

Sec. 8.11: More Advice From Sharpe Diversify. Economize. Costs matter. Personalize. Contextualize. (Too bad - Sharpe did almost the whole book without such ”management speak”!) Asset prices are not set in a vacuum”

And May I Add: We Have Seen... Inductive rather than deductive approach. Run experiments, andlyse results. When we let agents trade ’till equilibrium, there is a strong tendency for the market to end up in a situation where CAPM’ish results give a good description of prices. Portfolios, though, can differ a lot.

It’s not a zero-sum game: There are gains from trades – even from structured products. There are losses from ”poor structures” (Case 11.) But remain sceptical: Not everybody can beat the market. There are probably very few free lunches.