“If you give CAPM and VaR to monkeys, they are going to create financial crisis.” This is one of the most vivid sayings I have heard these days, although I believe that you also agree that “CAPM is the best paper over the past 20 years.”
Flawed Models, Bad Assumptions
Financial theories and books tell us that there are restrictions of Capital Asset Pricing Model (CAPM) and there are cases that Value at Risk (VaR) does not work for us:
- Risk averse investors who maximize their expected utility (one-period model)
- Homogenous expectations about asset returns (i.e. identical opportunity sets)
- Normally-distributed asset returns
- Risk free assets that can be borrowed unlimitedly at risk free rate
- Perfectly priced assets in a perfectly competitive and frictionless market with costless information
- No taxes, regulations, or restrictions on short selling
Investment banks introduced the idea of VaR but ironically regulators adopted the measure in the early of 2000, despite all the limitations of it:
- Often driven by short-run data
- Extremely vulnerable to peso problems
- Using historical data while history may not be a good indicator of future
- Conditioned on explicit estimates of correlation across risk sources and implicit assumptions about correlation, and the correlation estimates, again, are based upon historical data and are extremely volatile
- Unable to tell you about the size of losses within the 1% of trading days, i.e. maximum possible loss
- Different approaches and different assumptions result in different VaRs
Almost all the financial models we use are built up in mathematics, complexity, and supported by experts, professors, and authors of best sellers. We have been taught to use such flawed models with unrealistic assumptions, and we take these models to express realities, but we have neglected that realities are more impacted by market behaviors, which have not been figured out how to incorporate into our models.
The bad habit of finance people is that “WE LIKE COMPLEXITY.” In fact, the more abstruse the mathematics is, the more uncertain the results are. Rational investors do not invest in what they do not understand.
In finance, “Black Swans” are referred as “unpredictability, massive impact, and ex-post rationalization, which are impeded by all the behavioral finance terms: over-optimism, illusion of control, self-serving bias, myopia, and blindness.
What kind of models are we looking for? More Realistic models that count in illiquidity, leverage, bad behaviors, investors’ attitude towards rewards, incentives (e.g. discount the stream of liability at the risk of total asset, not the risk of liability), delegated management, and less complex mathematics; with financial innovation, such as social impact bonds, CDOs, buffered structured products, we aim to treat them with skepticism and always look for predictable surprises as well.
Market Efficiency and Random Walk
Efficient Market Hypothesis (EMH) suggests that at any given time, prices fully reflect all available information on a particular stock or market, which means the nonexistence of “anomalies.” In this sense, if one could be sure that a price would rise, it would have already risen; trading on available information fails to provide an abnormal profit.
In regression, Random Walk communicates the idea of “independence” that series whose successive returns are serially independent, assuming that one could analyze economic time series by extracting from a long-term movement, or trend, for separate study and then scrutinizing the residual portion for short-term oscillatory movements and random fluctuations.
The idea of stock prices following a random walk is connected to that of Efficient Market Hypothesis by scholars and researchers, “That no profit can be made from information-based trading leads to a random walk where the more efficient the market, the more random the sequence of price changes.”
Is the market efficient? In the stock market, investors tend to buy undervalued stocks and sell overvalued stocks, so in a market of many participants, the result can be anything but “efficient.” If market is efficient, how do we explain investors who have consistently beaten the market, e.g. Warren Buffett; if market is efficient, how do we explain the predictable patterns, such as “January Effect,” the “Wall Street Blue Monday,” and “Weekend Effect;” if market is efficient, then why risk premiums are not constant through time?
A Couple Thoughts on Risk Premiums
- I agree that value premium and size premium should be incorporated in the add-on models, as they are covariations of returns that cannot be diversified away.
- Price contains expected returns that bear market beta, but momentum is also a risk factor, it’s just that we do not know how to capture it.
- Given the current market condition and economic cycle, 5- to 10- year past performance basically tells us nothing; the last 35-year returns may give a better idea of risk premiums.
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