In his May 2007 paper entitled “Where Do Alphas Come From?: A New Measure of the Value of Active Investment Management”, Andrew Lo proposes a decomposition of the economic value of a fund’s management into two components, one measuring security selection (a weighted average of portfolio asset returns) and the other measuring timing (the correlation between portfolio asset weights and asset returns). When correlation between portfolio weights and returns is positive, management is moving assets toward optimization of overall portfolio returns. In other words, a manager can add value by: (1) picking the right assets; and, (2) continually growing positions with the highest future returns and shrinking positions with the lowest future returns. Using multiple examples, he argues that:
- If portfolio asset weights have no forecast power (zero correlation with returns), then the only sources of portfolio return are risk premiums available to passive holders of similar assets.
- Only the weight-return correlation contribution to performance, indicative of management’s forecasting ability, deserves the high fees typically charged by hedge funds.
- This measure is equally applicable to long-only portfolios, long/short portfolios and mechanical asset allocation rules. For example, if a manager shorts an asset, and the asset has negative returns, the correlation between the (negative) weight and the (negative) return is positive.
- It is critical that the sampling interval for portfolio weights and returns be at least as frequent as the weighting decision interval of the investment strategy.
The following charts, taken from the paper, illustrate the dynamic timing component of a fund manager’s value. They show different weighting strategies for a portfolio asset which yields a monthly return that alternates between 1% and 2%. The average monthly return for this asset is 1.5% for all three strategies.
The first strategy (top chart) applies a constant 75% weight to this asset. The average weight for this strategy is therefore, trivially, 75% across all months. The average monthly return from this asset is 1.125%. The manager for this strategy shows no understanding of the pattern of returns, and the correlation between monthly weights and monthly returns is 0.00. This manager may have picked a good asset but should not get a reward for informed timing.
The second strategy (second chart) alternates between weights of 50% in odd months and 100% in even months. The average weight for this strategy is also 75% across all months. The average monthly return from this asset is 1.25%. The manager for this strategy shows perfect understanding of the pattern of returns, and the correlation between monthly weights and monthly returns is 1.00. This manager should get a reward for informed timing.
The third strategy (third chart) alternates between weights of 100% in odd months and 50% in even months. The average weight for this strategy is again 75% across all months. The average monthly return from this asset is 1.00%. The manager for this strategy shows perfect misunderstanding of the pattern of returns, and the correlation between monthly weights and monthly returns is -1.00. This manager should be penalized for bad timing.
The paper provides context to these strategies by including a second asset for funds not applied to this one.
In summary, real active management consists not of the selection of portfolio assets but rather the decisions to change the weights of these assets within the portfolio.
Note that the strategies of averaging down/up as price falls/rises are attempts to manage the correlation between portfolio weights and future returns.
