QFIP 132 - What is an Index

Question 1

Modern index two main functions

Answer 1

1. Provide an aggregate measure of investment performance
2. Benchmark against which active managers can be compared

Question 2

Strategy Index definition

Answer 2

• A dynamic index that embodies a particular investment strategy
• E.g., Target-date funds, which dynamically change the allocation from equity to bonds as they approach the target date

Question 3

Deos a strategy index carries a sustainable risk premium?

Answer 3

• The efficients market hypothesis says an investment strategy cannot generate a consistent return in the market above the risk-return relationship defined by an equilibrium asset pricing model
• Competition and arbitrage suggests that “alpha” becomes commoditized to a level at which the returns are just enough to compensate investors for the risks associated with the strategy
• However, the dynamic properties of these risk factors and their expected returns require a framework other than the EMH’s static assumptions to interpret

Question 4

How to incorporate risk management in passive investing?

Answer 4

Using a dynamic index strategy that contains no alpha, but is actively risk-managed to a target level of volatility

Question 5

What is the other allocation of Index volatility control strategy

Answer 5

Remaing 1 - K_t will be invested in cash and earn risk-free rate

Question 6

What is the rebalancing frequency for Index volatility control strategy?

Answer 6

The rebalancing frequency for this strategy is normally daily

Question 7

An alternative way to estimate the volatility of an index

Answer 7

• Use an exponentially-weighted moving average (EWMA)
• lamda is a smoothing parameter that represents the weight given to the EWMA volatility estimate from the previous timestep
• S is the level of index

Question 8

How is realized volatility of the returns of volatility control strategy

Answer 8

close to the target volatility for index

Question 9

Backtest Bias

Answer 9

• Confusing a genuine investment performance in models with random estimation error from historical data when creating an optimal, risk-managed investment strategy

Question 10

Signal-to-noise ratio

Answer 10

• A measure used in science and engineering that compares the level of a desired signal to the level of background noise
• Ratio of useful information to false or irrelevant data

Question 11

Properties of active risk management strategies that make them prone to backtest bias

Answer 11

• The number of new products is growing rapidly
• Estimates for their performance are based on simulated returns

Question 12

Parameters for volatility control strategy

Answer 12

1. The rolling window length k for estimating short-term volatility
2. The upper bound of leverage, ¯l
3. The number of lags q for estimating short-term volatility

• Backtest biases also arise through the process of selection “optimal” strategy parameters