Investments, Mon. Feb. 4, '08

Investments, Mon. Feb. 4, '08

Investments , Wed. April 8, 09 Practical stuff: External forces (this time the admin) means that Tuesday April 21 is turned in unsupervised tuition. Youll get Hand-In #2 to work on. And well make it up from 8-9 on April 23 + 24.

I have posted two old exams and answers on the homepage. (This is the sum total in existence.) Today: Shapes Chapter 4. Focus: Pricing relations. If Chapter 3 looked like standard microeconomics to you, then Chapter 4 looks like standard asset pricing (though probably not to you).

But again, the fact that we get specific adds considerable twists. One way to express what the CAPM says: All investor returns depend only on the market return. And the dependence is linear. In Case 6 well see both these conclusions fail!

We start by looking at a bigger, more realistic financial market: 10 states(scenarios; telling names); note how there are one 5 market states (the intepretation is clear here; it isnt always). 5 assets (index funds; ditto) 2 agents (investors; ditto) The non-dependence problem is caused by incompleteness: Not all simple state

claims are traded. We will show that in a complete(d) market, investor returns do depend solely (and positively) on the market return (~aggregate consumption). First, well do it with APSIM; Case 7. Second, well do it mathematically/logically; Sharpe 4.4-4.8.

Third, we will go to incomplete models 4.9+ and start a journey towards pricing relations, formulas. Can we get CAPM? (Yes and/but thats not all.) Sharpes Sections 4.11 & 4.12 If there is a functional relationship (over scenarios) between price per chance and market return, R_M, then there exists (an economically meaniningful) pricing kernel,

f, and we get (as pure algebra) the relation E(R_i) r = b(i,M; f) (E(R_M) - r), where b(i,M; f) = cov(R_i,f)/cov(R_M,f). Economically meaningful means that there is a good chance that it will work well for the pricing of new securities, even in incomplete markets. Looks like CAPM to the casual observer. Its

not quite, because we need to know more about the exact nature of the functional relationship to get something really useful: Linear -> std. CAPM (Shaprpe 4.15-16) Log-linear -> power CAPM (Sharpe 4.17)

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