Theoretical Finance in Practice

1
Theoretical Finance in Practice

• By
• Andreas Humpe

2
The CAPM

• In practice the CAPM is often used in order to
  derive a weighted average cost of capital (WACC)
  .
• The WACC can be used to discount cash flows in
  the present value approach.
• Different bull and bear betas might be
  inconsistent.

3
Discounted Cash Flow (DCF) and the CAPM
4
The CAPM
Siemens-Beta vs. DAX Index between 1989-2008
estimated at 1.2
Source Bloomberg
5
The CAPM
Siemens-Beta vs. DAX Index between 1993-2000
(bull market) estimated at 0.99
Source Bloomberg
6
The CAPM
Siemens-Beta vs. DAX Index between 2000-2003
(bear market) estimated at 1.47
Source Bloomberg
7
The CAPM
Siemens Equity Risk Premium (Cost of Equity)
depends on beta.
Source Bloomberg
8
The CAPM
Source Bloomberg
9
The CAPM Cost of Equity

• The Problem
• CAPM-Betas often change over time.
• Different CAPM-Betas in falling raising markets.

• The Solution
• Assume a long-term mean reversion effect.
• Use common sense (industry, credit-rating,).

10
The CAPM (ß-Hedge)
MSCI Emerging Markets vs. SP500 between
2003-2007 estimated at 0.39
Source Bloomberg
11
The CAPM (ß-Hedge)
MSCI Emerging Markets fell twice as much as the
SP500 between 23.07.2007 and 16.08.2007
Source Bloomberg
12
The CAPM Beta-Hedging

• The Problem
• CAPM-Betas often change over time.
• Different CAPM-Betas in falling raising markets.

• The Solution
• Assume a long-term mean reversion effect.
• Use different CAPM-Betas for falling raising
  markets.
• Use common sense (country-rating, political
  stability).

13
The Optimisation
BARRA Optimisation
Source BARRA
14
The Optimisation
BARRA Optimisation to move original portfolio to
the efficient frontier
Source BARRA
15
Factor Portfolios Efficiency

• The Problem
• Factor portfolios (e.g. low P/E or high
  Dividend-Yield) might not be on the efficient
  frontier.
• Client requires low tracking error for hedging.

• The Solution
• Use of optimisation software to move the original
  portfolio to the efficient frontier line and
  minimise tracking error (or differences in the
  beta-factor).

16
Present value model implied earnings growth
rates
Goldman Sachs applies a present value model to
derive implied growth rates in the stock market.
They assume a fixed equity risk premium of 3 and
a terminal growth rate of 3.
17
Present value model implied earnings growth
rates
It seems that the long-term profit share to GDP
ratio is stationary. As a result the implied
earnings growth rate should be in line with
long-term expected GDP growth.
18
Present value model implied earnings growth
rates

• The Problem
• How much growth does the market price imply?
• Is the implied growth rate realistic?

• The Solution
• Use DCF to derive implied growth rate.
• Compare implied growth rate with history and use
  common sense to check accuracy.

19
Black-Scholes for Option-Pricing
Black-Scholes is often used for Option-Pricing in
practice
Source Bloomberg
20
Stock market returns are not normally distributed
Source Bloomberg
21
Black-Scholes for Option-Pricing

• The Problem
• Normality assumption.

• The Solution
• Use of jump-process assumption.