Category: Essential Concepts for Level II

11-12-19 Essential Concept 91: ETFs in Portfolio Management

Primary ETF strategies include: Portfolio efficiency: The use of ETFs to better manage a portfolio for efficiency or operational purposes. The applications include: transacting cash flows for benchmark exposure rebalancing to target asset class or risk factor weights filling exposure gaps in portfolio holdings of other strategies and funds temporarily holding during transitions of strategies or managers Asset class exposure management: The use of ETFs to achieve or maintain core exposure to key asset classes, market segments, or investment themes on a strategic, tactical, or dynamic basis. Active and factor investing: The use of ETFs to target specific active or… Read More

101 concepts level II

11-12-19 Essential Concept 92: Factor Models in Return Attribution

Active managers try to generate a return above a given benchmark by holding securities in weights different than the benchmark. The active return on a portfolio is the return on a portfolio minus the benchmark’s return. Multifactor models help us understand the sources of a manager’s return relative to a benchmark. Analysts favor fundamental multifactor models to decompose the sources of returns as they are easier to explain compared to statistical models. Using a factor model, we can decompose a portfolio manager’s active return as the sum of two components: Return from factor tilts: product of the portfolio manager’s factor… Read More

101 concepts level II

11-12-19 Essential Concept 93: Factor Models in Risk Attribution

Active risk, also known as tracking error or tracking risk, is the standard deviation of active returns. Tracking error is expressed as: where is the sample standard deviation of the time series of differences between the portfolio return and the benchmark return. The information ratio is used to measure active returns per unit of active risk. The formula for IR is given by: For example, consider a portfolio that has a sample mean return of 9% and the benchmark has a sample mean return of 7.5%. If the portfolio’s tracking error is 6%, then what is its IR? IR… Read More

101 concepts level II

11-12-19 Essential Concept 94: Value at Risk

Value at risk (VaR) is the minimum loss that would be expected to be incurred a certain percentage of the time over a certain period of time given assumed market conditions. Consider a $400 million portfolio. The VaR statement for this portfolio might be as follows: “The 5% VaR is $2.2 million over a one-day period.” Notice that the VaR measure has three important elements: Minimum loss – In our example the minimum expected loss is $2.2 million. The minimum loss can be expressed in either currency units or percentage terms. Time horizon – In our example the time horizon… Read More

101 concepts level II

11-12-19 Essential Concept 95: Sensitivity Risk Measures

Sensitivity measures determine how portfolio performance changes with respect to changes in a single risk factor. The different types of sensitivity risk measures are: Equity risk is measured by beta. Beta: Sensitivity of the asset’s return to the market risk premium. Interest rate risk of fixed-income securities is measured by duration and convexity. Duration: Sensitivity of the bond’s price to changes in its yield. Convexity: A second-order effect which measures changes in duration. Option risk is measured by delta, gamma and vega. Delta: Sensitivity of option price to the price of the underlying. Gamma: A second-order effect which measures changes… Read More

101 concepts level II

11-12-19 Essential Concept 96: Short-term rates and the business cycle

The price of a default-free nominal coupon-paying bond can be expressed as: where: = additional return required by investors to compensate for inflation = risk premium for uncertainty in future inflation With short-term nominal interest rates inflation uncertainty can be ignored and short-term T-bills can be priced as: Short-term nominal interest rates are positively related to short-term real interest rates and short-term inflation expectations. The interest rates are higher in economies with higher inflation and higher, more volatile growth. Central banks set short-term interest rates in response to the economy’s position in the business cycle. They cut rates when economic… Read More

101 concepts level II

11-12-19 Essential Concept 97: Yield Curves

The following figure show the UK government bond yield rates for July 2007, December 2010, and December 2011. From the yield curve, it is evident that the UK short-term interest rates were higher in 2007 than the long-term interest rates. There was a significant change (decline) in interest rates between July 2007 and December 2010. Yield curves have three characteristics: Level: views of future inflation determine the level. Slope: the magnitude of the risk premium determines the slope. The slope increases during recession. Curvature Most of the yield curve movement can be explained by changes in level followed by slope… Read More

101 concepts level II

11-12-19 Essential Concept 98: Decomposition of Value Added

A common way of decomposing value added is between value added due to asset allocation and value added due to security selection. Let us consider a portfolio of stocks and bonds where the weights allocated to stocks and bonds differ from the benchmark and each asset class is actively managed by selecting individual securities. The total value added due to asset allocation and security allocation is given by: The first term is the value added from asset allocation and the second term is the value added from security selection. Example: The following information is available for a portfolio comprising equities… Read More

101 concepts level II

11-12-19 Essential Concept 99: The Full Fundamental Law

According to the full fundamental law, the expected active return is expressed as: Information ratio is expressed as: The transfer coefficient is calculated as: It can take values from -1 to +1. If there are no constraints and the actual portfolio optimal weights are equal to the actual weights, then TC will be equal to 1 and we will have the basic fundamental law. The optimal amount of active risk in an actively managed portfolio with constraints is expressed as: The maximum value of the constrained portfolio’s Sharpe ratio is given as: Example: Consider an actively managed portfolio has… Read More

101 concepts level II

11-12-19 Essential Concept 100: Market Fragmentation

Market fragmentation occurs when the same instrument is traded across multiple venues. Markets across the world have become increasingly fragmented. Market fragmentation increases the potential for price and liquidity discrepancies. Electronic algorithmic trading techniques, such as liquidity aggregation and smart order routing, help traders manage the challenges and opportunities presented by fragmented markets. Liquidity aggregation involves creating ‘super books’ that present liquidity across all markets for a given instrument. This helps traders identify the best opportunities. Then smart order-routing algorithms are used to send orders to the markets that display the best-quoted prices and sizes.

101 concepts level II