From the weights and betas of three assets, compute the portfolio's weighted-average beta (βp).
Input Data
Results
At a glance:Portfolio beta is the weighted average of the individual asset betas, representing the portfolio's systematic risk relative to the market.
Formula
portfolioBeta = (weight1·beta1 + weight2·beta2 + weight3·beta3) / 100
$$$\\beta_p = \\sum_i w_i \\times \\beta_i$$$$$$0.5(1.2)+0.3(0.8)+0.2(1.5)=1.14$$$How to Use
- Enter each asset's weight and beta.
- Read the weighted-average portfolio beta.
FAQ
Why can portfolio beta be a simple weighted average?
Because beta measures systematic risk — the part that moves with the market — and systematic risk is linearly additive: the portfolio's sensitivity to the market equals the sum of each holding's sensitivity weighted by its share. This differs from volatility (standard deviation), which cannot be simply averaged because of cross-asset correlations; diversification reduces volatility precisely through lower correlation, but beta captures only the common market factor, so it adds up directly.
How do I use portfolio beta to manage risk?
It is a practical tool for tactical asset allocation. If you are bullish and willing to take more swings for higher returns, raise the weight of high-beta assets to push beta above 1 (aggressive); if the market is uncertain or you want defence, add low-beta (or even negative-beta hedge) assets to pull beta below 1 (conservative). For example, to lower beta from 1.14 to 1.0, cut the high-beta asset C and add the low-beta asset B. By adjusting weights you actively control the portfolio's market sensitivity to the level you want.
Must the weights add up to 100%?
In a standard portfolio the weights should sum to 100% so the beta reflects the whole portfolio. If you enter weights that do not total 100% (e.g. only some holdings, or cash held aside), the calculator still sums as the formula says, but the result represents only the beta contribution of the filled-in part, not the full portfolio. Cash is usually treated as near-zero beta, so holding cash lowers the overall beta. Include cash and any unfilled parts at beta ≈ 0 with their weights to get the true portfolio beta.
How does portfolio beta relate to the Treynor ratio or CAPM?
Portfolio beta (βp) and individual beta measure the same thing — systematic risk relative to the market — but βp is the weighted average of the holdings. Because systematic risk is linearly additive, βp = Σ(weight × beta), which lets you control the portfolio's market exposure by adjusting weights. It is used with other tools: the Treynor ratio = (portfolio return − risk-free rate) ÷ βp, measuring excess return per unit of systematic risk, so a correct βp feeds it directly; CAPM estimates expected return = risk-free rate + βp × (market return − risk-free rate), the risk premium for the portfolio's systematic risk, which you compare with actual return (Jensen's alpha); and in risk management/allocation, βp quantifies the portfolio's market sensitivity for active adjustment. In short, βp is the bridge between individual-asset risk and portfolio-level risk management, performance evaluation and expected-return estimation, and a key input to Treynor and CAPM.
Why can beta be averaged but portfolio volatility cannot?
This is a key and often misunderstood distinction. Beta can be weighted-averaged but volatility (standard deviation) cannot, because they measure different things and involve different treatment of correlations. Beta measures the 'moves-with-the-market' part (systematic risk) — each asset's sensitivity to the SAME market factor. Because all assets reference the same market, that risk is linearly additive, so βp = w₁β₁ + w₂β₂ + ... holds without considering how assets relate to each other. Volatility measures TOTAL fluctuation (systematic plus unsystematic). When you combine assets, total volatility is NOT a simple weighted average but also depends on pairwise correlations/covariances — this is exactly why diversification reduces risk: if two assets are not perfectly correlated, their swings partly cancel and the portfolio volatility is BELOW the weighted average. Lower (or negative) correlation means stronger cancellation. So portfolio volatility needs the covariance matrix, far more complex than a weighted average. In one line: beta only concerns the single 'market' dimension and is directly additive; volatility concerns 'how assets correlate and offset each other' and must include correlations — which is why diversification reduces volatility but not (the weighted-average) beta. That also explains why computing βp (what this calculator does) is simple while full portfolio-risk computation is far harder.
References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.