Value at Risk (VaR) measures the probability of underperformance by providing a statistical measure of downside risk. In the case of a continuous random variable, VaR can be computed as follows: $$ VaR\left(X\right)=-t \text{ where } P\left(X < t\right)=p $$…

Benefits of Multifactor Models to Investors Multifactor models help investors understand the comparative risk exposures of equity, fixed income, among other asset returns. This is done by performing a granular risk and return attribution on the actively managed portfolios. Multifactor…

Uses of Multifactor Models Multifactor models are mainly used for return attribution, risk attribution, and portfolio construction. Return Attribution Return attribution is a set of techniques used in the identification of the excess return of a portfolio, relative to its…

Active Risk Active return refers to the return on the portfolio above the return on the benchmark. That is, $$ \text{Active return} = R_P-R_b $$ Active risk, also known traditionally as tracking error or tracking risk, is a risk that…

Multifactor Model A multifactor model attempts to explain the observed historical return of security returns in the form of the equation below: $$ R_i=a_i+b_{i,1}l_1+b_{i,2}l_2+\ldots+b_{i,L}l_L+C_i $$ Where: \(R_i\) is the return on security \(i\). \(a_i\) and \(C_i\) are the constant and…

Single-factor Model The single-factor model assumes that there is just one macroeconomic factor, for example, the return on the market. Therefore: $$ R_i=E(R_i)+\beta_iF+\varepsilon_i $$ Where: \(E(R_i)\) is the expected return on stock \(i\). \(R_i\) is the return for stock \(i\)….

Arbitrage Opportunity Arbitrage is risk-free trading that does not require an initial investment of money but earns an expected positive net return. An arbitrage opportunity exists if an investor can make a deal that would give an immediate profit, with…

Counterparty Risks An investor’s principal can be put at risk by over-dependence on a counterparty. Moreover, the economic exposure of the fund can also be affected by counterparty failures. Therefore, investors are advised to evaluate the underlying counterparty risks when…

Some cost factors must be considered when trading in ETFs. They can either be implicit costs, e.g., tracking error, bid-ask spread, premium or discount to NAV, portfolio turnover, and secured lending; or explicit costs, e.g., management fees, commissions, and taxable…