tour of the mathematical concepts that are needed for acquaintance
with quantitative finance. Those readers who feel confident in their
mathematical background may jump ahead to Chapter 8.
Regarding further reading for this chapter, general introduction to
finance can be found in [6]. The history of development and valid-
ation of EMH is described in several popular books [9–11].
6
On the
MBA level, much of the material pertinent to this chapter is given
in [3].
EXERCISES
1. Familiarize yourself with the financial market data available on
the Internet (e.g., http://www.finance.yahoo.com). Download the
weekly closing prices of the exchange-traded fund SPDR that
replicates the S&P 500 index (ticker SPY) for 1996–2003. Cal-
culate simple weekly returns for this data sample (we shall use
these data for other exercises).
2. Calculate the present value of SPY for 2004 if the asset risk
premium is equal to (a) 3% and (b) 4%. The SPY dividends in
2003 were $1.63. Assume the dividend growth rate of 5% (see
Exercise 5.3 for a more accurate estimate). Assume the risk-free
rate of 3%. What risk premium was priced in SPY in the end of
2004 according to the discounted-cash-flow theory?
3. Simulate the rational bubble using the Blanchard-Watson
model (2.2.18). Define e(t) ¼ P
U
(t) 0:5 where P
U
is standard
uniform distribution (explain why the relation e(t) ¼ P
U
(t)
cannot be used). Use p ¼ 0:75 and R ¼ 0:1 as the initial values
for studying the model sensitivity to the input parameters.
4. Is there an arbitrage opportunity for the following set of the
exchange rates: GBP/USD ¼ 1.7705, EUR/USD ¼ 1.1914,
EUR/GBP ¼ 0.6694?
Financial Markets 15
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