TOPIC 1: Return Objectives Flashcards
Chapter 1 (Lustig)
What are the two key risk measures categories?
Absolute risk-standard deviation based - overall volatility or total risk of asset/portfolio (VaR, SD)
Relative risk-tracking error based - risk compared to a benchmark (beta, TE, IR), how much deviation from benchmark
Given the 2 known categories of risk measures…
Which risk measures fall under the 2:
Relative Risk:
* sharpe ratio
* information ratio
Absolute risk:
* standard deviation
* probability of loss
* average loss (negative returns)
* value at risk (VaR)
* maximum drawdown
* tracking error
Define tracking error, when its used and how to measure it:
Tracking error measures how consistent a passive portfolio strategy is in tracking or deviating from its benchmark.
Low tracking error: portfolio/manager is closely tracking the benchmark’s returns, minimal deviation (used in passive strategies)
High tracking error: portfolio is more volatile as it is deviating more from the BM, manager is likely taking more risk and there is greater chance of outperformance or underperformance (taken in active strategies)
TE = SD (Portfolio return - BM returns)
Define active vs passive strategy.
Passive Strategy: A passive investment strategy involves tracking a market index or benchmark with minimal buying and selling. The goal is to match the market’s returns rather than beat it, typically with lower fees. Common examples include index funds and ETFs. More stable, usually lower risk.
Active Strategy: An active investment strategy involves actively selecting securities with the goal of outperforming the market. This requires frequent trading, research, and market analysis to try and beat the benchmark. Active strategies often have higher fees due to management costs. Usually higher return and higher risk as well.
Can you define information ratio (IR), the formula and what type of investments its used in?
Information ratio is defined by:
excess return above the benchmark/tracking error
= active return/active risk
=alpha/σe
The IR would be used over Sharpe and VaR where FM wants to evaluate how well a portfolio is performing relative to a benchmark especially if they are trying to outperform a benchmark.
Define standard deviation risk measure:
Measures total volatility of the portfolio’s returns (how much the returns deviate from the mean return).
Define probability of loss:
Estimates the likelihood that a given portfolio will experience a loss over a specific period.
What is average loss (negative return)?
Represents the average amount of loss when the portfolio experiences a negative return.
What is VaR?
Value at risk: Estimates the maximum loss a portfolio could face over a given time period, at a specific confidence level (e.g., 95% confidence). Want to know potential loss in a worse case scenario, helps set risk limits and ensure capital preservation (‘no fund erosion’ -> USED FOR THIS RISK OBJECTIVE) a lower VaR means there’s a lower chance of loss
Define maximum drawdown:
The largest peak-to-trough decline in portfolio value, showing the biggest loss from a previous high to a subsequent low.
What is the benefit and disadvantage of using ratios?
Ratios are simple useful tools for evaluating past performance of investment or portfolio but they do not tell you if the success is from the skill or luck of the fund manager or user. Therefore it does not necessarily valuable for forecasting superior risk adjusted performance but can be useful to get a ballpark gauge of comparing options.
What are these short falls of return based analysis?
- benchmarks may not accurately reflect portfolio style (for example a mutual fund that invest in small Growth stocks is compared with the performance of the S&P 500 which is mostly large Stocks so it would give a misleading comparison as the fund might look like it’s out performing or under performing when really it should be compared to a similar index such as the Russell 2000 growth index)
- Return loading estimated with error and can be unstable : the estimated fact exposures (beers) are derived from historical return patterns which can be noisy and reliable over different time periods
- Waiting changed daily returns base ratios can estimate only average exposures, hence only providing a general approximation of exposure rather than precise real time insights
Take the results with a grain of salt as returns based analysis has inherent limitations and so it’s important to supplement with other methods such as holding based analysis to get more accurate picture.
What is the Sharpe Ratio indicate, what is it used for and what is the formula for it?
Risk-adjusted returns by considering total portfolio risk. It indicates the expected return generated per unit of expected volatility (total risk).
The Sharpe Ratio is used only in portfolio context, not for individual securities. Used when you want to know is the returns are good for the amount of risk taken.
Sharpe Ratio = [E(rp) - E(Rf)] / σp
What does a higher Sharpe Ratio imply? What does a lower sharpe ratio imply?
A higher Sharpe Ratio implies higher return per unit of risk (higher risk adjusted return), but not vice versa. A lower sharpe ratio suggests that returns may not adequately compensate for the level of risk taken.
What is a key comparison made using the Sharpe Ratio?
It compares portfolios that are appropriate for investment objectives such as capital preservation.
What is Jensen’s measure and when is it used?
Risk-adjusted performance metric evalauting the excess return of an investment relative to its expected return (CAPM) based on its beta. Essentially, excess return % after adjusting for systematic risk.
What does a higher vs lower Jensen’s alpha measure value signify?
A higher (positive) return means the portfolio is earning excess returns, suggesting skill of fund manager.
A lower Jensen’s measure value indicates poorer risk-adjusted performance, suggesting that the investment has underperformed relative to its risk.
What is the formula for Jensen’s Alpha?
alpha = (Actual Return - Expected Return) = Rp - [Rf + ß (RM- Rf)]
List one benefit and one downfall of using Jensen’s measure.
Benefit: It provides a clear indication of an investment’s performance adjusted for risk.
Downfall: It may not fully account for all risks or market conditions.
What is the formula for the required total return? (real)
Spending rate + real return - contributions + expenses
What is the formula for the required total return? (nominal)
Spending rate + inflation + real return - contributions + expenses
What is the formula for the required total return? Define each term.
Required Return = Spending rate + inflation + real return + expenses - contributions
- Spending rate: % of assets being spent over specific period
- real growth: expected increase in cost of goods & expenses
- fees/expenses: costs for admin and management related to the portfolio, reduces amount available for spending
- contribution: additional funds contributed to the endowment fund such as grants, donations, other incoming cash flow
What is the spending rule? Define and give the formula. Define each variable.
Spending(t) = y Spending (t-1) + (1-y)[theta Assets (t-1)]
- y = weight that determines proportion of spending carried from the previous period, i.e., how much current spending is influenced by past spending
- θ = determines the sensitivity of spending to previous assets (i.e., how much spending is driven by available assets).
- t-1 = spending or assets occurring in the previous period
- t = spending in the current period
What does a high vs low information ratio tell us?
IR > 0.5 (Acceptable) , above 1/2 (strong!) - adding value and risk is justified, suggests highly skill active management.
IR = 1 Decent performance, performance is justifying the risk taken
IR < 1 (weak performance) - excess return is not high enough to justify the risk, too volatile or underperforming to BM
Define volatility. High vs low values?
degree of variation in asset returns over time, aka standard deviation
higher –> Greater risk, potential for higher returns.
lower –> More stable, predictable returns.
Define beta. High vs low values.
sensitivity of a stock or portfolio to market movements, B=1 (moves in line with the Market)
high B (>1) –> More risk, but potential for higher returns.
low B (<1) –> Lower risk, more stable, defensive investment.
