Executive MBA
Theory of evaluation of investments

Outline of second day :

• Review of the equations of the CAPM (in a slightly different form) :
  • R_S = a_S + b_S * R_M + e_S
  • r_S = r₀ + b_S * (r_M - r₀)
  • var(R_S) = b_S² * var(R_M) + var(e_S)
• Elimination of e_S by averaging out into a portfolio of "similar" securities (securities with the same beta).
• Recommandation of CAPM :
  • "Playing" in the stock market is simple :
  • Choose the r_S you want, and invest into a portfolio of securities with the corresponding beta...
  • ...obtained from the plot of the Security Market Line : beta's in abscissa, r's in ordinate.
  • The SML is a simple transformation of the risk return graph where, along the abscissa axis, we plot the beta's instead of the standard deviation of the risk's (for a security, or a portfolio, with no specific risk e, we have std dev(R_S) = b_S * std dev of market profitability).
  • Or, more simply, invest part of your money into the market portfolio and the rest into TB
  • (or borrow money and invest it into M if you want more than the market profitability)
  • Remember that r_S will only be the expectation of your profitability (the actual profitability will be an outcome of R_S, which is itself linked to R_M by the relationship R_S = a_S + b_S * R_M + e_S).
  • If you want no risk, you have only one choice : treasury billls, with profitability r₀ (also denoted r_TB).
  • At present, in the US, r₀ = 4,5%.
  • Read also :
    • "Une économie américaine puissante mais fragilisée"
    • "Economists React To Fed's Rate Increase"
    • "Beijing master of the world economy"
  • After an interruption of 4 years, on Thursday 9 February, the US government issued again 30 year T-Bonds with an interest rate of 4,53%, and cashed in $14 billions. This can be interpreted as an anticipation of inflation, which will make this borrowing virtually free in the years to come.
• Efficiency and real markets
  • the standard "modern theory of finance" postulates that markets are efficient (information circulates freely, and everybody is able to appreciate the "real value" of securities)
  • (there are fine variations on this general definition)
  • in efficient markets, securities have zero NPV, and it is not possible to make money except by chance
  • but real markets are badly modelled by the "modern theory of finance"
    • real markets display bubble phenomena (since, at least, the Tulipmania bubble of the early XVIIth century)
    • prices come and go according to "crowd movements", and it is logical :
    • if it looks pretty sure that the bubble will still last for a while (like the price of gold in early 2006), it makes perfect sense to invest
    • therefore the dynamic of real markets is not that of efficient markets, it is more complicated
    • that is why there are so many people who play in the secondary stockmarkets
    • and some of them, applying pragmatic concepts of true "fundamental" value, do make money consistently (note that they hold their securities for a long time).
    • An example of "simple" complex dynamic system is the sinusoidal movement of cars on a freeway when the trafic is dense but still more or less fluid. It does not converge toward most efficient trafic regime which would be everybody driving at the speed of the flow where there is a squeeze. Similarly, markets are not efficient.
• Random variables : distinguish two situations
  • we know all the theoretical parameters
    • a past history is of no use
  • we don't know the theoretical parameters
    • a past history is useful : this is the case of finance
  • beta's are estimated from past joint history of R_S and R_M, they will be useful to estimate the opportunity cost of an investment
• The limitations of the CAPM theory.
  • In their 7th edition, for the first time, Brealey and Myers begin to mention Warren Buffett, and the Graham & Dodd approach to stockmarket investments
• Back to discounting :
  • the case of an investment with a single payoff in one year : IRR = plain usual profit
  • the IRR is the value of r such that NPV(r) = 0
  • this definition is naturally extended to several year payoffs
• Examples of calculations of IRR : I = (-100, 50, 80, 40, 10)
• Two important rates are attached to an investment :
  • an internal rate : the internal rate of return (in French : "le taux actuariel"). For the above investment, the IRR is equal to 35%
  • an external rate : the opportunity cost of capital. It is the yield of the firm into which the investment could be turned. Estimate the beta of the investment "as that of a stand alone firm", and compute r of the investment using the CAPM equation
  • this external rate is a consequence of the "no arbitrage rule" in financial investments
  • no arbitrage rule : two financial investments offering the same risk pattern must have the same profitability
  • when the risk pattern is higher, for the same future expected value, the price today is lower ; it can be shown to be a consequence of a "concave utility function of money" for investors, which translates in everyday language into the "risk aversion" of investors.
  • gamblers are not risk averse ; it cannot be shown to be a mistaken attitude. For instance if you have 100 euros in your pocket, and you desperately need 200 euros, otherwise you cannot obtain something very important to you, then it makes sense to bet your 100 euros in a lottery with payoff 200 euros with probability 10% and 0 euro with probability 90%.
• An investment is OK if and only if the opportunity cost of capital is smaller than the IRR
  • then, its NPV is the minimum value that its initiator can get by selling it
  • i.e. an investment with positive NPV creates "instant value" (not "value in the future", value now !)
  • General principle : maximise NPV
  • Limitations of this principle : people are not algebraic variables.
• The case of eBay and Skype.
  • Skype is a "key to a treasure trunk" for eBay.
  • calculations showing why eBay could pay up to $2,6 billion for a firm created three years ago, which reached about $60 mio of sales in 2005, and turned only losses.
  • this is an illustration of the fact that "calculating the value of a firm from its internal accounting and financial documents" is in general quite mistaken.
• The stock market offers only zero NPV investment opportunities (but one must invest its idle cash at least into risk free securities).
  • It is logical that an efficient stockmarket offers only zero NPV's :
    • we only exchange money for securities (it's a variety of swap)
    • securites have no interaction with our activities ; they are only paper value
    • (we don't even have the right to visit the firm which we partially own)
    • so they are sold for what they are worth, therefore no positive NPV
    • (people make money in the stock market either because they are lucky, or hold insider information, or identify non-efficient situations ;
    • and, in fact, real markets are not efficient, that is why Graham-like investors can make money consistently)
    • Day traders, when they have a keen sense of crowd psychology, can also make money in the market, with the exact opposite techniques from Graham & Dodd
  • To create value via an investment, we must acquire something which will interact with what we already own, i.e. make a "physical investment" (financial investment have zero NPV's)
    • if we buy two components and destroy both, we create negative NPV
    • if we buy two components that complete each other into a useful object, we create positive NPV
  • Idle cash must be invested at least into risk free securities
    • it can also be invested into risky securities, but in this case we swap risklessness for superior average return
• In the case of deflation, it is more advisable to invest one's money into TB with negative interest than to keep it in a bank.
• Special case of making an investment to kill it.
• Examples of DCF analyses to evaluate an investment :
  • various examples in class
  • sensitivity analysis
  • the polyzone example : an illustration of the power of DCF (forecasting future prices).
• Valuation of stocks : DCF of future dividends
• Perpetuities
  • with steady dividends
  • with growing dividends

Go to days 3 and 4