Portfolio diversification

Compare allocation and diversification

01 · Make a predictionAt fixed weights, how does lower correlation affect risk?

Asset A weight 60%

Correlation 0.2

A: return 8%, standard deviation 20%; B: return 4%, standard deviation 10%; annual assumptions.

Portfolio return6.40%

Portfolio standard deviation13.39%

A weights 0–100%; dot = current allocation. This curve is not an optimized efficient frontier.

Chart data

A weight	Return	Risk
0%	4.00%	10.00%
5%	4.20%	9.75%
10%	4.40%	9.60%
15%	4.60%	9.56%
20%	4.80%	9.63%
25%	5.00%	9.81%
30%	5.20%	10.09%
35%	5.40%	10.46%
40%	5.60%	10.92%
45%	5.80%	11.45%
50%	6.00%	12.04%
55%	6.20%	12.69%
60%	6.40%	13.39%
65%	6.60%	14.12%
70%	6.80%	14.89%
75%	7.00%	15.69%
80%	7.20%	16.52%
85%	7.40%	17.36%
90%	7.60%	18.23%
95%	7.80%	19.11%
100%	8.00%	20.00%

Weighted expected return

Rp = 0.6 \times 0.08 + 0.4 \times 0.04 \approx 6.40 %

Variance includes covariance; square root gives SD, in decimal-return units

σp = \sqrt{{0.6}^{2} \times {0.2}^{2} + {0.4}^{2} \times {0.1}^{2} + 2 \times 0.6 \times 0.4 \times 0.2 \times 0.1 \times (0.2)} \approx 0.1339

What did you just see?

When assets do not move together perfectly, some fluctuations offset. With perfect negative and equal weighted volatilities, modeled risk can be zero.

Keep observations consistent

Covariance equals times both standard deviations. Estimate it from aligned observations with matching frequency and return definitions, accounting for missing values.

Understand the units

Returns and volatility are displayed as percentages; variance and covariance use squared decimal returns. Annualizing risk requires additional time-independence and scaling assumptions.

Another example

Use the same observation horizon for both assets' returns and standard deviations.
Enter weights 60% and 40%, totaling 100%.
Return is 60% × 8% + 40% × 4% = 6.4%; variance including covariance is 0.01792.

Show formal definition and formula

Portfolio risk combines each asset's volatility and their co-movement; standard deviation is the square root of variance.

R_{p} = w_{A} R_{A} + w_{B} R_{B}; σ_{p}^{2} = w_{A}^{2} σ_{A}^{2} + w_{B}^{2} σ_{B}^{2} + 2 w_{A} w_{B} σ_{A} σ_{B} ρ

Rp: Expected portfolio return.
wA, wB: Nonnegative asset weights summing to 100%.
RA, RB: Asset returns measured over the same period.
σA, σB: Nonnegative same-period return standard deviations.
ρ: Return correlation, between −1 and 1.
σp², σp: Portfolio variance and its square root (standard deviation); no automatic annualization.

Common mistakes

Do not simply average standard deviations or mix monthly returns, annual volatility, and correlation from different samples. Historical correlations can change during stress.

Frequently asked questions

What is the correlation range?

It ranges from −1 to 1. One is perfect positive correlation, zero means no linear correlation, and minus one is perfect negative correlation; zero does not imply independence.

Can I short or use leverage?

This tool requires long-only weights totaling 100%. It does not model negative weights, leverage, dynamic rebalancing, transaction costs, or higher distribution moments.

You can now explore…

Compare how weights change return and volatility
Understand correlation and diversification

Term reference2 terms

Open a term when you need a reminder. Underlined words in the article work too.