Investing requires understanding of how the financial markets work and metrics that compare financial assets. In the following article, we give a brief introduction of the most used financial tools by investors.

Modern Portfolio Theory

evaluates the risk-return characteristics of an investment portfolio

Modern Portfolio Theory (MPT) is a framework for evaluating the risk-return characteristics of an investment portfolio. It was introduced in the late 1950s by Dr. Harry Markowitz and developed further in later years by Dr. William F. Sharpe and Dr. Merton Miller, eventually all three economists receiving the Nobel Memorial Prize in Economic Sciences in 1990.

MPT is the foundation for modern portfolio management and essentially is a tool to provide investors with reasonable expectations of the risk-return outcomes from an investment. Furthermore, the Mean-Variance analysis gives guidance to investors on how to create fully diversified portfolios by exploiting the imperfect correlations that exist between asset classes as well as individual assets within each class. This analysis creates optimal or efficient portfolios for rational investors, i.e. portfolios that will provide the highest expected return for a given level of risk, or the lowest level of risk for a given level of expected return.

The expected return in MPT is measured by the average or mean return while the risk/volatility/uncertainty is measured by the standard deviation of returns. Furthermore, MPT lies on some important assumptions such as the normal distribution of returns.

Sharpe ratio

measures the excess return of an investment above the risk-free rate per unit of risk.

Sharpe ratio, developed by Nobel laureate William F. Sharpe measures the excess return of an investment (above the risk-free rate) per unit of risk (measured by standard deviation). It can be thought of as a tool in comparing different investments, as returns alone are not a proper way of comparison. For example, returns of investment A can be bigger than the returns of investment B. But does that mean that is a better investment for the long-run? Not necessarily. The higher return might just be a compensation for the extra level of risk taken. That is why the Sharpe ratio is useful, as it measures the excess return that is produced per unit of risk. The higher the Sharpe ratio, the better the prospects of the investment.


measures the sensitivity of the asset's returns to the market returns.

Beta (β) is a measure of market or systematic risk of an asset or portfolio. Precisely, it measures the sensitivity of the asset’s returns to the market returns over a period of time. It can be measured using simple regression analysis. If the analysis is done in the US, the market can be represented by the S&P 500; in the UK, it can be represented by the FTSE100.

Values of betas can range from negative (in rare cases) to values lower, equal, or greater than 1. Negative betas imply that on average, the asset’s returns move in opposite direction to the market returns. Betas of less than 1 represent assets of lower risk than the market. Betas close to or equal to 1 represent assets that on average have the same systematic risk as the market portfolio, whereas betas greater than 1 are for assets than carry higher systematic risk than the market portfolio.

The main use of beta is to measure the systematic risk of a particular asset in order to predict its returns relative to the market portfolio. This is done through the Capital Asset Pricing Model (CAPM) developed by Dr. William F. Sharpe in the 1960s.

Although intuitive and useful, beta comes with some restrictions. First, it is measured using historical returns and we know that history is not necessarily a good predictor for the future outcomes. Second, it is time-varying and depends on the methodology used to compute it as well as the time horizon. And third, it ignores other sources of risk that might not be captured by the market risk but nevertheless need to be taken into account (these risks can be systematic but they can also be non-systematic or company-specific).


measures extra returns above the benchmark


Alpha (α) is a measure of the extra returns above the benchmark (or what an asset pricing model predicts) that can be attributed to the fund manager’s abilities to pick stocks/assets. Production of alphas is a justification of active portfolio management as opposed to passive portfolio management (i.e. investing in an index). The fund managers though will charge for this level of excess returns through higher management fees.

Alphas can be separated into fund and security alphas. Fund alphas are derived from the difference between the fund’s returns and the benchmark (S&P 500, FTSE 100, etc.). Security alphas are derived from the difference between the security’s actual returns and what is predicted by an asset pricing model (such as CAPM).

Critics of alphas (or active portfolio management) argue that the computation of those is based on models, such as CAPM, that rely on lots of unrealistic assumptions. Therefore, those excess returns can merely be a compensation for extra source of risk taken by the investors. Also, the fact that fund managers produced alphas for certain years might be due to luck and not sound judgement in investing. Finally, alphas are all about past performance and as we know, this is not always a good predictor for future outcomes.

Smart beta

combines advantages from low cost passive investments with intelligent asset selection

A long standing debate in the finance profession is whether investors are better off with active or passive portfolio management. Active portfolio management can produce alphas (returns in excess of the benchmark or what is predicted by a model) but usually comes with higher management and performance fees. Passive portfolio management is basically investment in an index fund and thus the return received is the market return (i.e. return received is compensation for the beta of the market). Passive investing though comes with a lower cost, as opposed to active investing.

Smart beta can be thought of as combining advantages from both strategies (low cost of passive investing, with the intelligent asset selection of active investing). The way that this is done is by constructing indexes in alternative ways to the traditional market-capitalization based indices. These alternative ways can be based on factors such as volatility, liquidity, quality, value, size and momentum.