Calculating Leveraged Portfolio Volatility from Weighted Returns
Summary
The document explains how to estimate portfolio volatility while accounting for leverage across assets. Its example combines each asset’s return with its portfolio weighting and account value to calculate the portfolio’s change in dollars, then expresses that change as a percentage of account value. Volatility is estimated from the resulting portfolio returns, so leverage affects the return series before volatility is measured.
An illustrative two-asset spreadsheet uses exposures of 100% and 50% of account value, then computes a rolling standard deviation and annualizes it. The author notes that the annualization factor must match the frequency of the data, such as one-minute returns. The account value is held constant in the example to keep the calculation simple. The method is an illustration rather than a complete treatment of risk: it does not discuss changing exposures, return correlations as a separate input, CFD-specific contract terms, or the suitability of a short realized-volatility window.
Key ideas
- Calculate portfolio returns by combining each asset’s return with its exposure weight and account value.
- Measure volatility on the resulting portfolio return series so leverage is reflected in the risk estimate.
- Choose an annualization factor that matches the sampling frequency of the returns.
- The example holds account value constant and does not address changing exposures or other portfolio complications.
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Full text
# Volatility of a leveraged CFD portfolio
# Volatility of a leveraged CFD portfolio
I want to calculate the portfolio volatility (as a weighted average of the products) and the portfolio consists of CFD contracts with multipliers ranging from 10 to 50 depending on the underlying product. The volatility is calculated as realized volatility of high-frequency (1 min) returns over a 15 minute period and does not take the leverage into account. I am wondering if I should incorporate the multiplier by multiplying the realized volatility by a corresponding multiplier. What I am ultimately interested in is having a portfolio volatility which also takes into the fact that an investor with higher leverages takes higher risk than an investor with no or low leverage.
## Answer by amdopt (score 2, accepted)
https://quant.stackexchange.com/a/39125
Here is an Excel example that I happened to have on my desktop. There are two assets (Asset1 and Asset2). Their respective weights are below their names. In this example, Asset1 has a "1" as the weighting (100% of the account value is exposed), and Asset2 has a ".5" (50% of the account value is exposed). The account is 1.5x leveraged.
The "Daily Change" column is: ([Asset1Return] * [Weighting] * [AccountValue])+([Asset2Return] * [Weighting] * [AccountValue]). You can add as many more assets as you wish.
The "5 Day RV" is basic: [STDEV.P([past 5 days])*SQRT(252)]. I only use 5 days and then annualize it to keep the example succinct. You can use as many periods as you want as well as change the Std Dev formula if you like. The SQRT(252) will need to be changed as well to account for you using 1 min data as opposed to daily data in my example (assuming you are trying to output an annualized number).
```
Asset1 Asset2 Daily Change Account Value Account % Change 5 Day RV Annualized
1 0.5 $1,000,000.00
1/2/2018 0.72% -1.14% 1475.492768 $1,001,475.49 0.15%
1/3/2018 0.63% -3.10% -9192.13069 $992,283.36 -0.92%
1/4/2018 0.42% 1.42% 11332.32292 $1,003,615.69 1.14%
1/5/2018 0.67% -0.35% 4909.580752 $1,008,525.27 0.49%
1/8/2018 0.18% -2.00% -8147.837357 $1,000,377.43 -0.81% 12.42%
1/9/2018 0.23% -1.56% -5520.996558 $994,856.43 -0.55% 12.82%
1/10/2018 -0.15% -0.85% -5787.739261 $989,068.69 -0.58% 11.92%
1/11/2018 0.73% 0.98% 12204.05017 $1,001,272.74 1.23% 12.39%
```
Note that for this example the [AccountValue] is held static at 1,000,000 to compute the "Daily Change". This example is only to show how you would compute the RV of a portfolio that has leverage included.
Hope this helps. Good luck.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.