Executive MBA
Theory of evaluation of investments

"It is essential to keep in mind that wealth is literally meaningless without future."
Peter L. Bernstein

Outline of first day :

• Accounting : transactions -> journal -> accounts -> adjustments and, then, synthetic documents (Income statement, Balance sheet, etc).
  • Monetary measurements.
  • Money is a complex concept.
  • Fiduciary money (like bank notes) has value inasmuch as other people will accept to exchange it for tangible value (value which we can consume)
  • You don't take bank notes to a desert island ; whereas you'll take value, which you can consume, with you.
  • Role of the public (monetary) authorities to maintain the purchasing power, and debt extinction power of money
  • Can only be done within a community with organised state institutions and powers
• What is tangible value ?
  • a violin, a sack of rice, a hammer, a pencil
  • If you own a violin and have no bow, a bow has a high value for you
• Money, Receivables and Securities
  • Money is a "public promise", guaranteed by monetary authorities
  • Receivables are "private promises", guaranteed by the signature of the issuer
  • Securities are
    • titles of property on tangible things, usually firms (shares of stock)
    • titles of property on promises (bonds, receivables, swaps, etc.)
    • there are many exotic variations upon this, to spread risk
    • generally speaking, a security is a contract : I give you something today, and I'm entitled to some (possibly) risky value coming from you in the future
    • by convention, securities have no tangible (usage) value, they are only rights onto some future payments
    • (that's why, we shall see, in a normal market, their NPV is always zero)
    • if they have some tangible value (like owning a whole firm) we no longer call them securities
• Book value vs market value, goodwill.
  • The market value of your firm is whatever price someone will pay you for it.
  • Accounting is not designed to measure market value.
  • The market value of your firm is not a function only of its economic performance, it depends upon the impact it will have on the purchaser's operations.
  • In other words, calculating the "value of a firm" only from its performance (earnings, dividends, etc.) is a limited exercise
    • you'll come up with its value in an efficient stockmarket where it is only a financial investment
    • but it may have a much higher value to some purchasers (cf. eBay and Skype)
  • Goodwill is the value recorded in the purchaser assets, to represent the difference between book value and acquisition price of a firm.
• Governments don't bother to publish a balance sheet with assets and liabilities
  • yet any economic agent has an accounting system with flows of value between inside and outside, an income statement per any period of time, and a balance sheet
  • examples of economic agents :
    • an individual, a household, a city
    • a firm, a bank, any group of people
    • a region, the gouvernment of a nation (acting on behalf of "the State"), federal governements, local governments, a continent
  • the French public debt is not 1100 billion euros, but 2000 billion euros
  • one must include provisions for future retirement payments already committed :
    • the money has already been paid to the State, but has not been put into any safe value haven
    • (some accountants even include future retirement payments of newly hired civil servants (in this case -> 3000 billion euros)
    • but it is spurious, because then their furure work should also be capitalized)
• Money vs value (i.e. cash vs value) :
  • accounting keeps track of value movements and value creation : selling something at a higher price than its value for us,
    • we can do this either because we incorporated our own labor into it (we added value)
    • or because, for some reasons, we, alone, had the possibility to put together elements, the association of which creates a useful thing
    • or because its value increased (thanks to increased demand) since we acquired it
    • we may have anticipated this third case ; it is then called speculation
    • the difference between the three cases is thin
    • it has disturbed philosophers and economists since Aristotle, including Thomas Aquinas and Marx
  • cash is only one aspect of value ; securities are value ; receivables are value (origin of modern accounting) ; inventories of goods are value ; fixed assets are value
  • but firms go under when they run out of cash, not when they make an accounting loss
  • that is another special aspect of cash :
    • it is some sort of proof of our creditworthiness
    • if we have or can borrow cash, we are creditworthy
    • if we don't have and cannot obtain cash, this means nobody trusts us anymore
• Balance sheet
  • the asset side of a balance sheet is concrete, the liability side more abstract
  • (think of viewing a bicycle, and think of whom it belongs to)
  • the liability side of a balance sheet records the origin of (accounting) value in our firm
• Income statement
  • a tentative representation of the production and consumption of value over a period of time
  • since value is not an absolute measurement, but is relative (a violin bow is very valuable to a violin player who has a violin and no bow, but is not valuable to a carpenter - except for resale...), accounting measurements of flows of value have a limited usefulness
• Purpose of finance : transform money into more money, in the future, and - even - now !
• Difference between accounting & finance : "the time value of money".
  • DCF analysis is the standard "Modern Financial Theory" tool to evaluate future cash flows.
  • There still is the "pragmatic" rule of "payback period" to recover invested cash.
  • In a nice theoretical framework DCF is flawless, but in real life it has drawbacks.
  • In many instances, the proper discount rate (the "opportunity cost of capital") is difficult to ascertain.
    • one has to figure out what are the "alternative opportunities with the same risk" and what is their best profitability
  • The discount rate is also a bit like the cost of releasing CO₂ in the atmosphere. In other words, it is difficult to analyse an investment totally disconnected from its environment.
  • The main flaw of the payback period method is that it does not take into account the "time value of money".
• Physical investments and financial investments
  • In a financial investment, we exchange money for titles of ownership of a firm (but we do not control the firm) or promises to be paid our money back, plus some specified extra value, at some future date
  • There are also more exotic financial investments where we exchange money for some complex possibilities of gaining more value in the future
  • A financial investment is an exchange of money for value with no interaction with our current activities
  • In a physical investment, we spend money to buy production equipment and to finance a working capital, in order to launch a project
  • A physical investment interacts with our labor, or activities, or private knowledge
  • Under normal economic conditions, only physical investments can create value.
• The standard graph of a security on a time line :
  • for a security S, we pay a price P_S today, and we sell it back for a sum X_S in one year
  • (X_S includes a possible dividend we may receive).
  • 
• Sure future payment vs unsure future payment.
  • only certain type of financial investments are riskless : short term bonds issued by governments of large prosperous countries
  • treasury bills (TB)
  • we still are under the threat of inflation, and exchange rate variations
  • other securities.
• The competition dilemma of states
  • they want to offer high short term rates on their TB, in order to attract loans and to make their currency attractive,
  • but they don't want to stifle the economic activity within their borders
  • at present (february 2006) the short term rate in the US is 4,5%
  • at present the short term rate in the euro zone is 2,25%
  • Because of the very large amount of US TB held by China, and the huge trade deficit of the US, the future of the dollar is in the hands of Beijing.
  • China will use its new economic and monetary power to impose its political and diplomatic choices.
  • In the Chinese subconsciousness there remain the unfair treaties of 1842, which were a consequence of the fact that, since Roman times, the East pumped monetary means from the West.
  • Now the West prints promises...
• Probability theory :
  • The standard toolbox to model risk attached to future value
  • Experiment
    • there is no well described probabilistic setting without a well described experiment
    • many paradoxes in probability come from some play on the experiment we are considering
  • Measurements of quantities which vary.
  • The simple maths to develop DCF theory.
• Random variables
  • Measurements which vary from one replication of the experiment to the next
  • Range of possible values
  • Distribution of probabilities (density, for continuous RV)
  • Series of past outcomes
  • Why most RV are normally distributed
• Expectation, variance and standard deviation of a numerical random variable
  • Expectation (or average, or mean) = weighted average of possible outcomes
  • well approximated by the simple average of a long series of past outcomes
  • a result in arithmetics. (The only axiom used is that symmetrical events have the same probability.)
  • Variance (and standard deviation) measures variability around the mean
  • Variance = Expectation of square deviation around mean
• Price of a security S, and profitability of a security : R_S = (X_S - P_S) / P_S.
  • The selling value X_S in one year (including the possible dividend) is modelled as a random variable generated by a random experiment
  • The year that will elapse between today and the same date in 12 months is thought of as the random experiment
  • The profitability R_S is also a random variable
  • It has a mean r_S = E(R_S) = [E(X_S) - P_S] / P_S
  • As a consequence, the following fundamental relationship holds too : P_S = E(X_S) / (1 + r_S )
  • Variations on this important equation play a fundamental role in DCF analysis
  • R_S has a standard deviation s_S = square root of variance of R_S = (standard deviation of X_S) / P_S
• Caveat : in finance, we meet percentages in two contexts
  • probabilities
  • profitabilities
• Mean profitability and risk of a security
  • Definition of the risk of a security : Risk of S = (by definition) s_S
  • Its present price P_S must be known in order to calculate s_S
  • otherwise we can only consider its risk pattern s(X_S)/E(X_S) and compare it to the risk pattern of other securities.
  • Only undiversifiable risk (see below) is taken into account to calculate a price today.
• Ibbotson data
  • 80 years of data on the profitability and risk of various kinds of securities in the NYSE
  • shows the positive relationship between risk and return
  • a  well diversified portfolio made of industrial stocks had an average return 9% above the TB rate, and a risk around 20%.
  • in a natural model, TB rates are not outcomes of a RV, but an external factor
• The series of prices of a security form a multiplicative random walk, not a series of independent outcomes of one RV.
  • Model of multiplicative random walk with yearly drift 13% and std deviation 20%
  • Starting from $1, the value, after n years, of a portfolio following such a random walk has a "log normal" distribution, that is, its logarithm is normally distributed with
    • mean = m times n (where m is the yearly "drift") ; here m = 13%
    • standard deviation = s times [square root of n] ; here s = 20%
  • (In this model, we approximate log(1 + R) with R, where R is the yearly profitability. The exact complete mathematical apparatus uses continuous stochastic processes.)
  • A presentation of random walks and derivatives by Mark Rubinstein
  • A retrospective on Markowitz's ideas for the 50th anniversary of his fundamental paper
  • Who's who in finance
• Risk return graph
  • abscissa axis : s_S
  • ordinate axis : r_S
  • 
• CAPM theory identifies, for any security, fundamental risk and specific risk (akin to an extra roulette wheel generated randomness)
  • fundamental risk (= market risk, = undiversifiable risk, = systematic risk, = risk which cannot be eliminated) vs...
  • ...specific risk (which can be eliminated by averaging out in a portfolio of "similar" securities).
  • It is a mathematical result in linear algebra of RVs
  • TB have zero risk, zero variability. Their return is the minimum (average) return one can get in the market. And it is sure.
• CAPM main results
  • One central portfolio is the "market portfolio", denoted M
  • M is well approximated by any well diversified portfolio of 20 to 40 securities (eg : S&P portfolio, DJ portfolio)
  • Define, for any security S sold in the market, b_S = covariance(R_S, R_M) / Var(R_M)
  • It is approximated by the slope of the straight line fitted, with the appropriate method, through a scattergram of past outcomes of (R_M, R_S)
  • R_S = r_TB + b_S (R_M - r_TB) + e_S
  • We say that S moves "like the market" with a "reactivity factor" b_S, plus an extra random term e_S the mean of which is zero.
  • Let's look at the expectation of R_S (denoted r_S)
  • r_S = r_TB + b_S (r_M - r_TB)
  • Let's look at the variance of R_S (denoted s²_S)
  • s²_S = b²_S * s²_M + Var(e_S)
  • The part b²_S * s²_M is called the undiversifiable risk of the security S
  • A portfolio made of a few securities is also, itself, a security
  • A central idea of CAPM is to "average out" the diversifiable part of the risk of securities of same b by pooling them into portfolios
  • Remember, if you throw one die, you will get a random result with mean 3,5 and std dev 1,7. If you throw several dice, the average result won't change but the std dev of the average result will be reduced.
  • beta of any security S is estimated from past history of S and M, and published by agencies like Merrill Lynch.
  • 
• The concept of discounting
  • A piece of paper promising that we will receive, from its issuer, $100 in one year, is not worth $100 today. It has a price today which depends upon the creditworthiness of the underwriter. At best, it is worth 100/(1 + 4,5%) = $95,7.
• Fundamental no-arbitrage rule in finance :
  • In a normal (efficient) market, two securities having the same expected value with the same standard deviation (taking into account only the non diversifiable variability), in one year, must have the same price today
  • Slight extension : two securities having the same risk pattern s(X)/E(X) in one year must yield the same profitability
  • This result enables one to compute the price of a proposed security when we know the profitability of another one with the same risk pattern (taking into account only the non diversifiable variability).
• Profitability and IRR
  • IRR is the natural extension to a stream of several cash flows of the common concept of profitability.
  • Invest $60 today and get $75 in one year : profitability = 25%
  • Invest $60 today and get $30 in one year, $30 in two years, and $20 in three years.
  • What is the "profitability" ? It is not (80 - 60) / 60 !