LITMIR.BIZ

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did this happen?

      Every trader should have a thorough understanding of phenomena such as predatory trading and manipulation; and of liquidity problems that can arise when traders position themselves in a similar fashion to one another. These problems are often understood intuitively, but there is a benefit from understanding the theory behind them and from seeing the evidence of how they work.

      In this book, after setting the scene in the first chapter, I look at predatory trading, crowded exits, stop losses and manipulation. In each case, I consider the risks and opportunities that arise for traders.

      Chapter 1. The Ecology of Markets

      Fair value

       What is the right price for an asset?

      A common way of thinking about this problem for a security, such as a stock or a bond, is in terms of its fair value. This is the notion that there is a single value that the security is intrinsically worth at any given time.

      A rigorous way in which to think about the intrinsic value of a security is to consider the future cash flows that the security will generate for the owner, and then discount those cash flows back to today’s money. This concept relies on the idea that an expected cash flow at some future date is less valuable than money in hand today, because of the opportunity cost of not having access to the cash today, and the risks associated with future events. Where an investor or trader knows the future cash flows from a security for certain, and knows the rate at which to discount them, calculating the fair value of that security is simple – a few lines of work on a spreadsheet.

      But, in practice, things are not so easy.

      Consider, for example, a bond issued by a highly credit-worthy government. The cash flows are documented in the bond’s prospectus and are known almost with certainty: each regular coupon payment and the return of principal at maturity of the bond are highly likely to transpire. So far, so simple.

       But what is the correct discount rate?

      Ambiguity over the appropriate discount rate makes it difficult in practice to estimate the fair value of a security. Analysts develop techniques for coping with this problem – one of the most popular of which is taking the implied discount rate from similar securities, and using this to discount the cash flows from the security in question.

      Now consider a riskier security, such as a corporate bond. In this case, the cash flows to the bond’s owner are less certain, as default risk is now higher. Consequently, the intrinsic value of a corporate bond is thus (generally) more difficult to evaluate than for a government bond.

      And difficulties do not end with corporate bonds.

      Equities offer greater problems – think about the unreliability of cash flows and dividends attributable to shareholders. An extreme example would be, say, a biotechnology company, where cash flows might be zero for the foreseeable future and in the long-run might depend upon success in developing new drugs. Long-term cash flows could be huge…or non-existent!

      Uncertainty over both cash flows and the appropriate discount rates leads to great uncertainty over the fair value of a security. Two analysts, each using the same theoretical discounted cash-flow approach, could place very different values on the same security, depending on their cash-flow projections and the discount rates they choose to use. Because of such ambiguity over the true value of a security, some analysts dismiss the notion of a fair value. Instead, they think of securities as having observed market prices and estimated cash flows, and simply use the implied discount rate in the market to compare securities to one another.

      Many financial models assume a fair value exists

      Whether or not it is sensible in practice to think about the fair value of a security, a number of financial models assume that there is such a thing as the fair value of a security. A quick trawl through published articles and working papers on asset pricing reveals that this is a very popular assumption in academic work. Some models go further still: not only do they assume that there is a fair value to a security, but this fair value is known with certainty to some market actors, such as arbitrageurs. But how do the arbitrageurs know the fair value of a security? Most papers are mute on this subject.

       Why would a model-builder make such an assumption?

      Mainly because it creates a framework for thinking about markets which, through further analysis, can provide illumination on how markets work. The assumption that fair value can be known with certainty might come as a surprise to some arbitrageurs. To know the fair value for say, a stock, seems like a hopelessly unrealistic assumption. However, academic work sometimes makes simplifying assumptions, to reduce the complexity of a situation, and to make the mathematics more tractable.

      According to Friedman (1953), the use of unrealistic assumptions does not invalidate the work, so long as the predictions are accurate. Thus, the notion of a fair value that is known to some, but not all, market actors is a simplifying assumption to help us understand the actions of arbitrageurs and the workings of markets. It is worth bearing this in mind when looking at financial models that rely upon such assumptions. Models can provide illumination on how markets work, but a trader must avoid the mistake of relying wholly upon the predictions of models.

      The problem of simplifying assumptions

      Some asset-pricing models make a further, important simplifying assumption about the process of arbitrage. They assume that traders can short-sell securities as easily as they can buy. For example, a widely-taught asset pricing model, known as the arbitrage theory of capital asset pricing (Ross, 1976), assumes that there are no restrictions on short-sales, including full use of the short-sale proceeds. However, in practice, short-sellers must find securities to borrow, effectively pay securities lending fees and face collateralisation and margin requirements. These short-sale constraints limit the frequency and scope of arbitrage, and so could affect the price of assets.

      So, we know that some models that seek to explain the pricing of assets make use of unrealistic simplifying assumptions.

       Does this matter?

      Are the predictions from such models accurate, or do they instead fail the ‘Friedman test’ that I mentioned earlier? In a canonical paper on short-selling constraints, Miller (1977) considers what happens to security prices if the two main assumptions discussed above are untrue at the same time.

      While popular models such as the capital asset pricing model (see Sharpe, 1964) assume that investors have identical estimates of the expected return and probability distribution of returns from all securities, Miller suggests that investors in practice can have differing expectations about securities instead, due to uncertainty over future cash flows and the appropriate discount rate for an investment. He argues that when a divergence of opinion amongst investors is combined with barriers to short-selling, the price of a security is no longer set by the average investor, but instead by the beliefs of the most optimistic investors. Those investors with the most optimistic estimates of returns will own the securities, while pessimists and realists struggle to short-sell the overpriced asset because of constraints on short-selling. Miller concludes that

      the presence of a substantial number of well informed investors will prevent there from being substantially undervalued securities, but there may be securities whose price has been bid up to excessive levels by an uninformed minority.

      This provides a simple explanation for why some securities might trade at inflated prices. Even if informed traders or investors know the fair value of a security, other less-informed traders push the price beyond that level, and it is difficult to short-sell the security back to its fair price. Mis-pricing develops because of ambiguity over fair value; and arbitrageurs are unable to correct the anomaly if there are barriers to short-selling.

      A number of researchers have investigated Miler’s idea. Although there is some dispute over its implications, Asquith et al. (2005) state

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