### In Search of Alpha: Quant Investment Strategies

__I____n Search of Alpha: An Analysis of Quantitative Investment Strategies__

The game of blackjack has been played in casinos for centuries, and until the 1960s seemed to be a game that was impossible to beat. It was not until the advent of scientifically and mathematically sound papers, such as *The Optimum Strategy in Blackjack*, published in the Journal of the American Statistical Association in 1956, that beating the house became a theoretical possibility. Indeed, it was thanks to the suitably titled *Beat the Dealer* by Ed Thorp, that accomplished blackjack players began to post consistent returns against the house. After making small fortunes in the casinos of Las Vegas, some of the foremost mathematical masterminds decided to take their theories to the biggest gambling stage of all: Wall Street.

Up until this period in the early 1970s, Wall Street investors were typically characterised by the likes of Benjamin Graham and Warren Buffett – pioneers of the value investing strategy. Over the coming years, trailblazers such as Ed Thorpe, Peter Muller and Ken Griffin would usher in a new generation of Wall Street traders, adopting quantitative investment strategies to generate active returns on their investments, or *alpha* for short.

__Modern Portfolio Theory__

Modern Portfolio Theory (MPT) is a mathematical system introduced in 1952 by Harry Markowitz in his Nobel Prize winning essay *Portfolio Selection*. MPT allows investors to allocate and diversify assets in a portfolio such that the anticipated return is maximised for their given level of risk tolerance. One insight provided by the theory is that an investment’s risk and reward should be viewed in the context of the portfolio as a whole, rather than considered individually. For example, when constructing a portfolio an investor should bundle securities together such that if one security falls in value, another rises by an equal amount, allowing the investor to offset their loss. However, during bullish market conditions, the portfolio rises with the market, generating return for the investor. MPT includes complex statistical measures such as correlation and variance to calculate the optimal allocation of assets in a portfolio. Markowitz plotted the risk and return of combinations of assets to arrive at an *efficient frontier* – a set of optimal portfolios offering the highest expected return for a predetermined level of risk.

The ultimate conclusion of Markowitz’s work is that diversification is essential to reducing risk. Whilst systematic (market) risk is inherent in owning a stock, exposure to specific (company/industry) risk can be minimised through a varied portfolio.

Critics of the theory question its accuracy because of its reliance on historical data, reminding us of the adage that past performance is no guarantee of future results. MPT makes calculations of future performance using historical measurements of asset return and volatility, often neglecting to take into consideration circumstances that may have evolved since the data were generated. Further, opponents criticise the theory’s probabilistic approach to risk management, quantified by the likelihood of losses, whilst giving no consideration to the reasons why such losses may occur.

__Black-Scholes Model__

The Black-Scholes formula was developed by economists Fischer Black and Myron Scholes as an options pricing model. Options are contracts giving the buyer the right to buy or sell an asset at a specified time at a pre-agreed ‘strike’ price. The formula incorporates current stock prices, the strike price, time to expiration, volatility and the time value of money to calculate a theoretical value for European style options.

The formula has underpinned significant economic growth up to the present day, with 50 billion underlying shares being traded through options contracts in 2007. One of the features that made it such a success was its inclusion of parameters that do not rely on historical data. Unlike in Modern Portfolio Theory (mentioned above), data such as current stock price, strike price and time to expiration are incontrovertibly observable, leaving little margin for inaccuracy. Despite its success, the influence of the Black-Scholes Model has been partially blamed for the financial crisis of 2008. The Black-Scholes led to the invention of increasingly complex financial instruments whose value and risk profile became progressively more incalculable. This culminated into collateralised debt obligations, with risky ‘junk’ bonds concealed inside, that led to the crash of 2008. The model has since been refined, notably by Robert Merton, for which Scholes and Merton received the Nobel Prize -Black died 2 years before the prize was awarded.

Despite the model’s accuracy at pricing options, critics have voiced their objections at some of the considerations that the formula neglects, such as taxes and transaction costs. The model also requires that it is possible to buy or sell any amount of stock, which may not always be a realistic assumption.

__The Efficient-Market Hypothesis__

Efficient-Market Hypothesis (EMH) was a culmination of works dating back to the 1900s. It was finalised in the 1960s by the Chicago finance professor Eugene Fama. The EMH was based on the idea that security prices follow a *random walk*, and that the current price is representative of all known information about the security. In essence, the chances of a security rising or falling are as random as the toss of a coin.

Fama’s theory implied that technical analysis, using past price trends to predict future prices, cannot be used to outperform the market, because past prices have no effect on the random price movement of a security. Given that the EMH states that all publicly available information is incorporated into a security’s price, the theory also negates the use of fundamental analysis to generate *alpha*. These conclusions suggest that it is impossible to purchase undervalued or sell overvalued securities – in essence, it is impossible to ‘beat the market’, and worthless to invest in actively managed funds. This led to the founding of passively managed funds, pioneered by John Bogle, founder and retired CEO of The Vanguard Group.

Despite the success of the EMH, the theory undermined the work of value investors such as Graham and Buffett, attributing their success to sheer luck. Whilst Buffett himself is a proponent of the EMH, can one really amass a wealth of $73 billion through good fortune alone? Other objections to the theory arose during the Black Monday crash of 1987. The Dow Jones Industrial Average fell 23%, which according to calculations using Fama’s EMH was a ‘statistical impossibility’. Yet, most of all, it was antagonistic to the conquerors of Las Vegas; if they could beat the dealer, who says they couldn’t beat the market too?