Consolidating Strategy Weights to Calculate Portfolio Volatility
Summary
The document asks how to combine multiple strategies into one portfolio and why volatility calculated from aggregate asset exposures may differ from volatility calculated using strategy return streams. It describes two views: treat each strategy’s returns as a portfolio component, or combine the strategies’ underlying asset weights and calculate risk from the asset covariance matrix.
The response confirms that the asset-level method uses the standard portfolio variance relationship: first form consolidated asset weights as the weighted sum of each strategy’s holdings, then apply the covariance matrix. The example illustrates this aggregation by multiplying each strategy’s portfolio allocation by its within-strategy asset weights and summing the resulting exposures. The response does not derive the discrepancy or discuss practical complications such as differing return timing, leverage, cash, or constraints, so equivalence depends on weights and return streams being aligned and represented consistently.
Key ideas
- Combine strategy portfolios by multiplying each strategy’s asset weights by its portfolio allocation and summing across strategies.
- Calculate consolidated portfolio variance from the resulting asset weights and the asset covariance matrix.
- The strategy-level and asset-level approaches should correspond when exposures, returns, and weights are aligned consistently.
- Differences can arise if the compared return streams and underlying exposures do not represent the same portfolio conditions.
Tags
Full text
# Volatility Estimation # Volatility Estimation Let say I ran two strategies and got its weights at each rebalance and equity curves. I would like to combine these systems to get the performance if I were to trade them concurrently from a portfolio level. The first way to do it would be to just take the equity curves of the respective strategies and treat them as asset class return streams and allocate weights at desired rebalance. To get the performance, I simply do w'R, where w = weights at each rebalance and R being the returns of the strategies. If I were to calculate portfolio volatility given weights w, I would simple employ p.risk = w'E w. The second way to do it, is to first calculate the get the desired weights for each strategies. From there I can drill deeper and get the weights of the asset classes for each strategy. (assume they trade the same universe) But the problem here is that when I get the aggregate exposure for each asset class and calculate portfolio level volatility (using w'Ew (of asset classes)), I get a number that is less than the first way of doing it. Why is that? Should both methods be the same, all else equal? example of second way Each strategy trades Asset1 and Asset2 at first rebalance: Strategy 1 allocated 30% Strategy 2 allocated 70% Within each strategy: Strategy 1 allocates 10% to Asset1 and 90% to Asset2 Strategy 2 allocates 60% to Asset1 and 40% to Asset2 To get portfolio level asset exposure simply: ``` Strategy1: x= asset 1 (30%*10%), asset2 (30% * 90%) = 3% , 27% Strategy2: y= asset 1 (70%*60%), asset2 (70% * 40%) = 42%, 28% Aggregate Asset 1 exposure = 3% + 42% = 45% Aggregate Asset 2 exposure = 27% + 28% = 55% for a total of 100% ``` So given asset1 = 45% weight and asset2 of 55% weight, I can simply get portfolio risk by w'Ew where E = covariance between the two assets. ## Answer by SRKX (score 1) https://quant.stackexchange.com/a/8226 Yes, you can definitely use the classic $\sigma^2=w' \Sigma w$ formula to compute the volatility. In fact, you first compute your consolidated portfolio $w_p$ from your two strategies portfolios $w_A$ and $w_B$ by giving them weights weights $\alpha_A$ and $\alpha_B$ as follows: $$w_p = \alpha_A \cdot w_A + \alpha_B \cdot w_b $$ Then the variance is calculated for $w_p$ as it would for any portfolio.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.