23
THE DISCOUNT RATE

Investors invest money today expecting more back in the future. But the important question remains: even if you can pin a number on what those future dollars might be, what are they actually worth today? Well, to work this out there are a couple of issues to address.

Firstly, there's the issue of inflation. In an inflationary environment, a dollar buys less in the future. Until the middle of the 20th century negative inflation (deflation) was as common an event as inflation; that is, there were periods when things got cheaper to buy. But in more recent decades it's been different. For the past 70 years, in fact, there's been a general expectation that prices will march forever upwards. This presents problems when placing a current value on future cash flows. Predicting future inflation rates can never be more than an educated guess. And, as with predictions of future earnings, it's a guess that's heavily influenced by the rate of inflation prevailing at the time the analyst is coming up with the estimate.

Secondly, there's the issue of the risk associated with the particular investment being valued. Investors are being asked to exchange something that is certain (cold, hard cash held today) for something that is far from certain (future cash flows based on the business prospects of the company).

The dollar-reducing effect of inflation and the potential dollar-reducing risk of investing in a substandard business are both embodied in a single figure called the ‘discount rate' — the rate that is applied to estimated future cash flows to convert them into today's dollars. The higher the expected inflation, the higher the discount rate. The higher the anticipated company risk, the higher the discount rate.

Let's now consider how a discount rate is applied. A 5 per cent discount rate means that a dollar delivered in one year will be worth 5 per cent less than a dollar is today — that is, 95 cents. And a dollar delivered in two years will be worth 90.7 cents (95 cents less 5 per cent).

Okay, we've now covered Valuation 101. By now you've likely twigged to the magnitude of the problems we're facing. For starters, we don't know what future levels of inflation (or deflation) will be. And we have no way of quantifying risk since we don't know how the business will perform in the future. We want to apply this indefinable discount rate to indefinable future cash flows. And, just to add complexity to uncertainty, there can never be a single discount rate appropriate for all companies or for any single company over time.

But again let's relegate these problems to the back seat. In our efforts to feed the needs of the real world, let's press on. We'll start by looking at a couple of people who thought long and hard about the problem and eventually came up with their version of a mathematical solution.

THE CAPITAL ASSET PRICING MODEL

The story of the Capital Asset Pricing Model (CAPM) begins with a 25-year-old graduate student at the University of Chicago called Harry Markowitz. In 1952 Markowitz released a research paper entitled ‘Portfolio Selection', in which he argued that investors should view investment risk in terms of their entire portfolio, rather than the individual stocks within that portfolio. And that was fair enough. It was a long-held belief that it was risky to ‘put all your eggs in one basket' by investing in only one stock.a

But it was how Markowitz went on to define risk that was novel: he related stock price movement to a statistical term called ‘covariance', which could describe how the prices of two stocks move in relation to each other. If their prices or returns move together, they have a ‘positive covariance'. For example, if the iron ore price increases, this is great news for all companies that mine iron ore. Other things being equal, the stock prices of all companies that mine iron ore should rise. They are described as having high positive covariance. The same news should also be positive for companies supporting the mining industry, such as producers of explosives and mining equipment. They would be said to have a positive covariance with the iron ore producers, although the covariance might be lower than that between the iron ore producers themselves.

On the other side of the coin, two stocks are said to have a ‘negative covariance' when their share prices move in opposite directions following the release of certain news; this may apply, for example, to oil stocks and airline stocks. If the price of oil goes up, the news will be positive for oil stocks and negative for airline stocks (heavy fuel users). Markowitz incorporated these concepts into a model defining the trade-off between risk and reward. Ultimately his concept became widely accepted, and for his work he was awarded the Nobel Memorial Prize in Economic Sciences in 1990.

Markowitz believed the optimal balance between risk and reward was to be found in a diversified portfolio, but not just any diversified portfolio. He developed a formula for defining the optimal mix of assets within a portfolio, and when his formula was traced out as a graph it presented as a curved line referred to as the ‘efficient frontier'. Build a portfolio that sits anywhere on this line and you have the optimal balance between risk and reward. So ‘Modern Portfolio Theory' was born.

Others worked to develop Markowitz's ideas. His initial formula was difficult for people to get their heads around and cumbersome to use. It was also time consuming to calculate and, considering the limitations of computing power at the time, expensive to calculate. Enter a brilliant young economist called William Sharpe. Sharpe whipped Markowitz's theory into the simplified working formula we now refer to as the Capital Asset Pricing Model (CAPM).

Sharpe's 1964 breakthrough was to take Markowitz's concept of equating risk with stock price movement and to simplify how it was measured. To do this he compared each stock's price movement not to other single stocks but to those of a well-diversified portfolio. And what more appropriate example of a diversified portfolio could there be than the entire stock market?

Sharpe's revision of Markowitz's formula meant it was now simple to use, and it provided a practical way for analysts to pin an actual number on risk. Armed with this number, investors felt they were now able to price derivatives, determine the intrinsic values of stocks, and construct better performing and less risky portfolios.

The CAPM can be stated as follows:

Required return on a particular stock (discount rate) = Current expected risk-free rate + β (equity risk premium)

There are three inputs to the CAPM formula:

  • current expected risk-free rate
  • equity risk premium
  • beta (β).

These three inputs can be thought of as three layers of return and risk. The first layer is the return you would expect from a ‘risk-free' investment. The second layer is the extra return (the return above the risk-free rate) you would expect from holding a broad-based portfolio of stocks. And the third layer is the extra risk associated with holding just one stock, the stock you're calculating the discount rate for. Let's discuss each.

The risk-free rate

The risk-free rate is the interest rate attached to sovereign debt (money that a government has borrowed). Take it that the risk-free rate relates to the bonds of fiscally responsible governments. (The fact is that governments occasionally blow themselves up by borrowing too much — the Spanish, Greek and Italian stock analysts, for example, were hard pushed to come up with a figure for their risk-free rate during the 2010–13 Euro debt crisis.) But in the case of the US the thinking is that you can lend to Uncle Sam and there's a good chance you'll get your money back. In choosing between the interest rates on short-dated Treasury bills (‘T-bills') and long-term government bonds, many argue it's more appropriate to use the 10-year bond rate since it better represents long-term return expectations. And that's more in line with the returns delivered by stocks, since they're also long-term investments.

But are bonds actually a ‘risk-free' investment? Sure, they provide a near guaranteed return if you hold them to maturity. But remember Markowitz's own definition of risk: he equated risk with price volatility, and the market prices of 10-year bonds can demonstrate extreme volatility over the short term.

I still remember the first day I walked into the Bankers Trust dealing room in Melbourne in 1987. My role on BT's dealing desk was to trade bank bills, and the typical maturity of these debt instruments was 90 days. Unless interest rates changed significantly, the value at which they traded didn't change much. Sure, their price varied over the 90-odd days they were on issue, but not significantly. They were always soon to mature. And when they did, bank bill investors would simply roll over their investment at the new rate. Nothing much gained, nothing much lost. Fairly capital stable, little stress, little excitement.

But it was a whole different story up the other end of the dealing room, where the bond traders were sitting. I soon realised that those boys got a lot more excited when interest rates moved. At first I was confused — my impression was that bonds were boring instruments. Buy a 10-year, put it in the bottom drawer, and collect the interest payments every six months until it expires sometime in the distant future. Why were these guys getting so excited?

The penny dropped when I eventually learned how to price a bond. I discovered that because interest payments are fixed (that is, the interest payment or coupon doesn't change when interest rates do), a move in interest rates necessarily impacts the price investors are prepared to pay for the bond. And the period to maturity is like a lever on price — the longer the bond, the bigger the price move. I realised these guys up the other end of the trading room were playing with highly volatile instruments. If bond traders made a wrong move they could lose their shirt. So, relating this back to the CAPM, which equates risk to price volatility, how can long-term bonds be presented as a risk-free investment under its definition?

It seems to me that CAPM applies a different definition of risk to stocks than it does to bonds in order to facilitate a convenient solution to a difficult problem. To derive a discount rate in the CAPM, Markowitz, Sharpe and their disciples were defining the ‘risk-free' nature of bonds as ‘non-default'. Yet the ‘risk' of holding stocks was being defined differently — not as the risk of default but rather as the volatility of price and return.

Before I leave this part of our discussion of the CAPM, I just want to give an example of Warren Buffett's perception of its usefulness, or should I say lack of usefulness. The CAPM suggests that lower interest rates deliver lower discount rates, and these should lead to higher stock valuations when plugged into valuation formulae. It's intuitively appealing because in a low interest rate environment investors chase the yields of stocks down, and hence their market prices increase. It's not surprising then that the following paragraph, from Robert Hagstrom's book The Warren Buffett Portfolio, caught my attention:

Buffett tells us that, in a low interest rate environment, he adjusts the discount rate upward. When bond yields dipped below 7 percent, Buffett adjusted his discount rate up to 10 percent. If interest rates work themselves higher over time, he has successfully matched his discount rate to the long-term rate. If they do not, he has increased his margin of safety by three additional points.128

By using a higher discount rate when interest rates are historically low, Buffett is allowing for the increased chance that interest rates could rise and that stock prices could fall. It's a reminder that we should be thinking in terms of ‘mean reversion'. Just because interest rates are abnormally high or low at the time of the valuation doesn't mean they'll always remain that way.

The equity risk premium

On to the second input: the equity risk premium. The CAPM says that stocks are a riskier bet than government bonds, so a premium needs to be added to the ‘risk-free rate' delivered by bonds to reflect this. Intuitively you'd think this premium would be easy to calculate. After all, stocks and bonds have been traded for centuries, and reliable records of stock prices, stock indices and their relationship to bond rates have existed for more than a century. Just compare the difference between the historical returns on holding stocks versus bonds, right? Unfortunately, there are a few problems with what would seem to be a good idea. Let's list them:

  • What period do you choose for the comparison? Because the premium has varied through time — a lot.
  • What broad-based equity index do you use for the comparison?
  • What government debt instrument(s) do you use for the comparison?
  • What country do you look at? Because the premium has varied from one country to the next — a lot.
  • Are historical comparisons even relevant? After all, it's the future that matters in investing, not the past.

Got the idea? It just isn't possible to nail a single figure on the equity risk premium.

Beta

Beta is the third and final input to our CAPM-determined discount rate, and it requires a bit of explanation.

Beta compares the risk of holding a single stock (the one we're ultimately trying to derive the discount rate for) to that of holding a broad-based portfolio of stocks. It measures the sensitivity of a single stock's returns to those of the broad-based portfolio. A beta of one means the returns from holding the single stock vary the same as for the broad-based portfolio. A beta greater than one means the single stock returns vary to a greater degree; less than one and it's more stable. A beta of zero means there's no relationship between the returns of the two. So the use of beta is supposed to be the factor that adjusts the equity risk premium (which has been calculated for the broad-based portfolio of stocks) into a risk premium specific to the single stock you're attempting to value.

Are there any problems with this approach? Absolutely. Beta is a statistical measure, and the stock market doesn't dance to statistics.

Markowitz would have been better served if he'd taken note of the earlier writings of US economist Frank Knight and British economist John Maynard Keynes.

In 1921 Knight released a groundbreaking book titled Risk, Uncertainty, and Profit. He argued that financial markets are characterised by ambiguity — that is, future uncertainty. Risk in financial markets is unquantifiable because a set of future outcomes cannot be defined, nor could probabilities be assigned to them were it possible.

Let's demonstrate what Knight is saying through an example. You have a pair of dice, and you throw one of them across the table. What's the chance a five will come up? Easy: one in six. How do you know this? Because, as Knight has said, you can define the set of possible outcomes (1, 2, 3, 4, 5 or 6) and you can apply probabilities to each outcome (equal probabilities, or one in six for each outcome). Without these two prerequisites you can't define outcomes statistically. But, as Knight also states, neither is definable in the stock market. Possible outcomes? Near limitless. Assignment of probabilities to each outcome? Who knows!

Keynes added to the argument in his 1921 book A Treatise on Probability. He stated that probability cannot be measured purely from observed frequency. If you flip a coin many times it's unlikely to demonstrate a pure 50:50 outcome. It's more likely that the outcome will be something approximating that ratio. Yet anybody, if asked, would say the expected outcome of a coin toss is 50:50 heads or tails. Indeed I can guarantee that any book on statistics will state that the odds are 50:50. Keynes justified the discrepancy between outcome and theory by stating that probabilities are based on expectations, not on actual outcomes.

Having taken this on board, now consider the probability of a stock market crash occurring next week, next month or next year. No idea? Join the queue. We're incapable of placing probabilities on stock market outcomes. Keynes summarised this concept succinctly in The General Theory: ‘It can easily be shown that the assumption of arithmetically equal probabilities based on a state of ignorance leads to absurdities.'

What then of actuaries working for insurance companies? Don't they apply probabilities to unknown future outcomes? Do their actions deny what Knight and Keynes are saying? After all, when you set off for a journey in your car isn't the future ambiguous, uncertain, unpredictable? You can't predict whether you're about to have a car crash. To use Keynes' words, isn't this outcome preceded by ‘a state of ignorance'? Yet somehow insurance companies are able to calculate the odds that accidents will occur and then use these to price insurance policies.

But there is one sizeable difference between motor accidents and the stock market. There are over one billion cars on the road. Car accidents are governed by the law of high numbers. There are plenty of statistics to splice, dice and dissect. And while the insurance companies can't use past observations to predict the future with absolute accuracy, they'll come close enough to enable them to turn a profit on the insurance policies they write. Compare that with the financial markets, which experience a decent fender-bender only every decade or two.

Put it all together and you'll find that beta is not a proxy for risk, as many academics wish us to believe.

Short-term price volatility is a risk only to short-term traders. To investors, price fluctuations don't present a risk but rather an opportunity. Just ask any hardcore investor how they feel about a stock market crash: they love it, seeing it as an opportunity to buy cheap stocks. Yet this is a time when volatility, the academic's proxy for risk, goes through the roof. The academic's position is that a stock that has fallen significantly in price has a high beta.

But to an investor the same stock, under the same circumstances, might represent great value and therefore less risk. The investor's argument intuitively makes more sense.

The dictionary defines volatility as ‘a liability to change rapidly and unpredictably'. I would say that sums up what stock markets do most of the time. Markowitz equated risk to price fluctuation. Now I don't know whether Markowitz read The Intelligent Investor, but Graham held a very different view on the matter, stating that stocks ‘should not be termed “risky” merely because of the element of price fluctuation'.129

To my mind Graham was right. What's more, he delivered this conclusion after several decades of experience operating in Wall Street. He had a razor-sharp mind and a penetrating sense of logic. In contrast, Markowitz, when he first came up with his concept of risk, was a young university student with no financial market experience. In his attempt to find an interesting topic for a thesis, he chose to quantify the unquantifiable. His equations were ultimately presented to a finance profession that wanted to believe in them. It was a convenient attempt to resolve an inconvenient problem.

As an additional consideration, volatility is representative of both upward and downward price movements, but financial market risk is unidirectional — it is the risk of losing money. As New York University's Peter Carr said of price volatility, ‘It is only a good measure of risk if you feel that being rich then being poor is the same as being poor then rich.'

As noted, fluctuating share prices, to the seasoned investor, represent opportunity not risk. This was the premise behind Graham's classic tale of Mr Market and has been the bedrock of Buffett's stock purchases for Berkshire Hathaway for decades.

A case in point is the movement of the Chicago Board Options Exchange Volatility Index (VIX) during the GFC. Based on the implied volatility of 30-day options on the S&P 500, it reached its highest recorded levels at the very time the US stock market was offering its best buying opportunities for years. It's a perverse investor who thinks buying sound assets at cheap prices is associated with higher levels of risk.

Because volatility is a short-term concept it's understandable traders would interpret volatility as being at least partly representative of risk. But, unlike traders, investors give themselves the luxury of time, and with time the relevance of volatility diminishes.

There is no single measure of risk or single discount rate that is applicable to a single company through time. Changing debt levels, new competitors, shifts in technology and alterations in economic conditions mean these measures are an ever-changing thing. In response to this concern, Nobel laureate Robert Merton set about developing a dynamic version of the CAPM dubbed ‘the intertemporal capital asset pricing model'. While Merton has a great mind, his model did not prevail over the insurmountable.

History has virtually forgotten Cambridge academic A.D. Roy. Like Markowitz, he published an article on portfolio theory — interestingly in 1952, the same year Markowitz published his. Despite being conceptually similar, it is Markowitz, not Roy, who has been credited as the father of Modern Portfolio Theory. It is interesting then to hear Roy's comments after reviewing Markowitz's 1959 book, effectively a publication of his 1952 thesis:

While Dr. Markowitz warns that past experience is unlikely to be a very good guide to future performance, he gives us no clear indication of how either we, or our investment advisers, can provide ourselves with sufficiently precise or generally agreed expectations to merit their processing in an elaborate way …

Mr. Markowitz presses for a precision in the specification of both motives and of expectations which it seems unlikely that any existing investor can reasonably be expected to possess or to express coherently.130

So let's summarise where we're at with the CAPM, our academic attempt to determine a useful discount rate. Remember that:

The required return on a particular stock = Current expected risk-free rate + β (equity risk premium)

It states that the discount rate applicable to the stock varies with the risk-free rate (government bond rate). To borrow the CAPM's own terminology, it assumes a positive covariance between stocks and bonds. I'd suggest that this relationship is not so direct. The reality is that the covariance can be positive or negative, high or low, depending upon the mood investors and central bankers are in at any point in time. The next variable, beta, is a hypothetical figure that does a poor job of describing reality. And the ‘constant' — the equity risk premium — is not a constant at all.

BARR ROSENBERG'S BARRA

Berkeley graduate Barr Rosenberg was interested in risk, and particularly in how it could be modelled and measured, so naturally his attention turned to the CAPM. Common sense told him, as it told most people, that the risk of holding a stock is influenced by many more factors than variations in its market price. What about the type of industry it operates in, its capital structure, the diversification of its customer base, the quality of management and the threat of competition — just to name a few. Based on his academic insights, in 1973 Rosenberg formed the consulting organisation Barr Rosenberg and Associates; the name was subsequently shortened to BARRA.

BARRA developed computer programs that, among other things, attempted to predict a stock's beta using numerous inputs. The investment industry felt Rosenberg was on to something, and his list of clients grew. Rosenberg left BARRA in 1985 to start a portfolio management business, but in 2011 he was found guilty of securities fraud and consented to a lifetime securities industry bar. The Securities and Exchange Commission disclosure stated he had concealed ‘a significant error in the computer code of the quantitative investment model that he developed and provided to the firm's entities for use in managing client assets'. More specifically, the error disabled one of its key components for managing risk.

Given the difficulty in deriving an appropriate discount rate let's now investigate how variations in the discount rate impact our valuation.

SENSITIVITY OF THE DISCOUNT RATE

You might be thinking I'm exploring this whole discount rate issue a bit too thoroughly. After all, does it really matter whether you use a discount rate of 5 per cent or 6 per cent when calculating a stock's value? The answer is yes, it does matter. What appears to be a small shift in the discount rate can have a significant impact on the valuation. To demonstrate, I'd like to introduce you to the Gordon Growth Model, named after financial economist Myron J. Gordon. I'll be discussing it at length in the next chapter, but at this stage I'll use it simply as a useful platform for discussion. The Gordon Growth Model is a simple valuation formula that requires just three inputs:

images

where:

  • V0 = stock value
  • D1 = estimate of next year's dividend
  • r = discount rate
  • g = growth rate of dividends.

Using this simple formula let's test the impact on the valuation of a change in the discount rate. To do this we'll first keep the dividend and dividend growth rate constant. Assume the company being valued will pay a dividend of 10 cents next year and that the dividend will grow at a rate of 4 per cent every year after that. If a 10 per cent discount rate is used, the formula value will be:

images

However, if a discount rate of 8 per cent is chosen, the formula value is $2.50. Changing the discount rate from 10 per cent to 8 per cent has resulted in a 50 per cent increase in the valuation. Let's see what happens when we start playing around with the other inputs as well.

First set of assumptions:

  • Next year's dividend: 10 cents
  • Discount rate: 10%
  • Dividend growth rate: 2%
  • Formula value: $1.25

Second set of assumptions:

  • Next year's dividend: 11 cents
  • Discount rate: 8%
  • Dividend growth rate: 4%
  • Formula value: $2.75

So with what we thought were small adjustments to our inputs we see a 120 per cent lift in our valuation.

MORE PRACTICAL MEASURES OF RETURN AND RISK

Okay, so I've punched a lot of holes in the CAPM, but we still need a figure for the discount rate to plug into our formulae. To me it makes sense to ignore the insurmountable problems listed above and simplify our approach to choosing an appropriate discount rate. And to make it official let's also make a name change. Let's now refer to the discount rate as the ‘required rate of return' or ‘RRR'. This is the minimum rate of return we demand our investment to deliver. We set the rate by considering our alternatives — the returns being delivered by other investments.

It's also the way the two kings of common sense, Warren Buffett and Charlie Munger, have resolved the issue. I was at the 2014 Berkshire Hathaway AGM, along with 39 000 other people, when Buffett addressed the issue. He described the process of selecting a discount rate as ‘what can be produced by our second best investment idea. And then we aim to exceed it. In other words it's an opportunity cost'. Munger added: ‘Cost of capital is defined in a very silly way in business schools.' While not specifically stating it, Munger was clearly referring to the CAPM and the weighted average cost of capital.

In assessing investment risk I prefer not to think about beta, the CAPM and other theoretical concepts. I'd rather focus on real-life risks. And the first risk, since we're talking about money, is the risk of losing it — either some of it (receiving either a substandard or negative return) or all of it (if the company you've invested in goes bust).

There are three ways you'll end up receiving a substandard return:

  • by paying too much when you buy
  • by selling at a low price
  • by receiving a low dividend stream during the time you own the stock that isn't sufficiently compensated for by capital gain.

So this type of risk can be distilled down to price, price again and income. To minimise this risk, buy cheaply, sell at a premium, and buy companies that are not only financially sound but produce lots of cash.

You might have noticed the discussion has now become a bit circular. We started by attempting to quantify risk so we could value the stock; that is, risk was an input to stock valuation. But we've now turned things around to say price is integral to the determination of risk!

Let's now consider the risk of the company going broke. There's no need to think like a statistician here — just think like a banker.

You've got capital at risk, so don't hand it over to Shonky Brothers Ltd. As I've previously said, I don't want this book to turn into a tome on financial analysis, so I won't delve deeply into techniques of determining creditworthiness. Just remember that as a stock holder you're standing at the end of a pretty long queue. For example, if the company goes down, you're behind the bankers. So, in theory, your assessment of creditworthiness should be more thorough than theirs. The main issues in judging a company's creditworthiness are:

  • too much debt. As Ben Graham used to say, ‘A company should own at least twice what it owes.'131
  • strong cash flow. Don't accept what the Income Statement in the annual report is telling you — get to know your way around the Cash Flow Statement.
  • the viability of the company's business model.

That's all I'm going to say here, but if you want to explore the subject of debt and risk further then I refer you to appendix B. Let's turn instead to another concept of risk — one that also doesn't rely on abstract mathematical theories.

The risk of being human

Financial markets haven't been around long enough to influence the way humans think; in evolutionary terms we've barely left the African savanna. Our behaviour is driven by the same instincts of survival found in every other species on this planet. In the face of unacceptable danger we choose to run. Accordingly, when financial markets collapse our natural instinct is also to run — that is, to sell. We reinforce one another's natural instincts, meaning we buy and sell with a pack mentality. So when investors are doing dumb things, like selling when stock prices are down, many others tend to do exactly the same. The problem is this isn't exactly market-beating behaviour.

Financial markets are bedevilled by the counterintuitive. For example, risk in financial markets is actually at its lowest when everyone believes it's high. The time of greatest risk is when few perceive it. Ironically it's a time usually characterised by a sense of unbounded, blind optimism — something that has preceded every stock market crash since equity markets began. Here's a quote from Joseph de la Vega's Confusion de Confusiones describing the mood immediately before Holland's wealth-destroying stock market crash in 1688:

… on the Exchange, a goodly supply of money and abundant credit were available; there were splendid prospects for exports; a vigorous spirit of enterprise; brilliant military forces under famous leaders were [protecting the country]; there was favourable news, incomparable knowledge of business, a swelling population, a strong fleet, advantageous alliances. Therefore not the slightest concern, not the least apprehension reigned, not the smallest cloud, not the most fleeting shadow was to be seen.132

So familiar was finance writer Henry Hall with the optimism felt by investors just prior to a stock market crash that he described the buoyant mood prior to the 1907 Panic as being of ‘the old, old way'.133

Blind optimism followed by stock market crashes is still how events pan out today, and most likely always will. The question often asked is: why does the mood change so quickly? What's the trigger that causes investors' enthusiasm to be switched off and panic to be switched on?

Applying logic to answer this question seems to be a waste of time, but applying logic is exactly what every inevitable post-crash inquiry attempts to do. The reasons start rolling in: monetary policy was too tight, monetary policy was too loose. In 1907 it was an earthquake. In 1987 it was a storm in the UK. No, it was programmed trading in the US. No, it was changes in tax policy. Market manipulation, leverage, you name it — everything has at some stage copped the blame. Interestingly the common culprit, unrealistic and unbridled pre-crash optimism, barely rates a mention. Yet it should. Howard Marks nailed it when he said: ‘I'm convinced that it's usually more correct to attribute a bust to the excesses of the preceding boom than to the specific event that sets off the correction.'134 This is not dissimilar to a comment made by Graham in The Intelligent Investor as to a principal cause of the Great Depression: ‘The extreme depth of the depression of the early 1930's was accounted for in good part, this writer believes, by the insane height of the preceding stock boom.'135

When six major investigations failed to come up with a credible reason for the 23 per cent collapse in the Dow Jones Index on 19 October 1987, it was Bob Shiller who offered the best explanation. In surveying investors as to why they sold that day, the common response he found was that they were reacting to the crash itself. In other words, they sold because everyone else was.

Here then we have the reality. Markets can climb due to a wave of contagious, unbridled enthusiasm. And they can collapse due to a wave of contagious, unbridled fear. This is something no formula can quantify.

Since risk is at its greatest when most market commentators are telling us conditions are great, and at its least when they are telling us not to invest a dime, I don't take my cue from commentators. I take my cue from the actions of grey-haired and wealthy investors who've been through a stock market cycle or five. This is one of my favourite quotes, taken from Henry Clews' Fifty Years in Wall Street, first published in 1908:

If young men had only the patience to watch the speculative signs of the times, as manifested in the periodical egress of these old prophetic speculators from their shells of security, they would make more money at these intervals than by following up the slippery ‘tips' of the professional ‘pointers' of the Stock Exchange … I say to the young speculators, therefore, watch the ominous visits to the Street of these old men. They are as certain to be seen on the eve of a panic as spiders creeping stealthily and noiselessly from their cobwebs just before rain.136

FURTHER INPUTS — THE CO-STARS

So now we've covered the two main inputs to valuation formulae — the same two inputs demanded by Pisano's eight-centuries-old discounted cash flow formula: cash flow and discount rate. But many valuation formulae ask for inputs other than these. This might seem strange, since the formulae are supposed to be working out the same thing — until you realise these other inputs are simply a different way of expressing the same information. So before we move on to looking at the formulae there are just two more inputs I want to discuss — book value and return on equity.

Book value

I defined book value back in chapter 15 but it's worth a quick refresher before we move on to the next chapter.

Book value is taken from the Balance Sheet in the company's financial accounts (also referred to as the Statement of Financial Position). It's calculated by subtracting what a company owes (total liabilities) from what it owns (total assets). It's also referred to as net assets or shareholders' equity.

In theory, book value indicates how much shareholders would receive if the company were to be wound up on the date the accounts were constructed — what's left over after everything is sold up and all debts paid off. I say ‘in theory' because financial statements are accounting constructs and therefore they often differ from economic reality.

Book value is commonly expressed on a per share basis. This is calculated by dividing the total book value of the company by the total number of shares on issue.

Return on equity

Return on equity (ROE) measures the rate of return the company delivers on the book value or shareholders' equity. For example, if the book value per share is one dollar and the company returns a profit after tax of 15 cents on every share, the return on equity is 15 per cent. It measures the return shareholders are receiving on the money they've tied up in the company, and it assists them in judging whether their return expectations are being met.

Many formulae ask for book value and return on equity as inputs. Does using them enhance our ability to value stocks? No, it doesn't. Remember the trouble we had in determining what future cash flows will be? Remember our concerns about extrapolating historical figures into the future? Remember the questions we raised about using net profit after tax as an input to our valuation formulae? Using return on equity and book value resolves none of these concerns because:

Net profit after tax = Return on equity × book value

So let's now move on to the formulae themselves.

Chapter summary

  • To bring future cash flows back to current dollar values, they need to be adjusted using a discount rate.
  • The Capital Asset Pricing Model (CAPM) is a mathematical method that has been developed for deriving discount rates. It can be summarised as: current expected risk-free rate + β multiplied by (equity risk premium).
  • Government bonds (sovereign debt) of fiscally prudent countries have low default risk but do demonstrate significant price volatility. The price volatility of bonds increases as the term to maturity increases, all other things being equal.
  • The equity risk premium varies both with the study period and the country being considered.
  • Beta is a statistical measure, and the stock market doesn't dance to the tune of statistics. Beta isn't a proxy for investment risk, as some academics wish us to believe.
  • Risk is often high when many market participants perceive it to be low, such as just before a stock market crash.
  • Beta increases both during a stock market crash and in its aftermath, yet this is often the time when value investors perceive the market as having its lowest level of risk.
  • Volatility is representative of both upward and downward price movement, but financial risk should be described by loss, which is asymmetric.
  • Warren Buffett doesn't believe that the CAPM is based on sound principles. He judges the cost of capital to be the opportunity cost of capital — in other words, the return he could have achieved by employing his second best investment idea.
  • The discount rate can also be described as the required rate of return (RRR).
  • Valuations are sensitive to the discount rate applied.
  • A significant risk in financial markets is behavioural risk.

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