Portfolio Volatility: How More Assets Reduce Risk

Imagine you are carefully building a balanced collection of different investments, like creating a diverse garden instead of just planting one type of flower. This is similar to constructing an investment portfolio. Let’s think about what happens to the overall ‘wobbliness’ of this garden, or in investment terms, its volatility, as you add more and more different types of flowers, assuming each flower’s growth is independent of the others.

Volatility, in the world of investments, is like the degree to which your investment’s value bounces up and down over time. A highly volatile investment is like a rollercoaster, with dramatic ups and downs. A less volatile investment is more like a gentle, steady incline. We often want to reduce this ‘wobbliness’ because large, unexpected drops can be unsettling.

Now, let’s consider a portfolio where we’ve carefully chosen many different investments, and for simplicity, we’ve allocated an equal amount of money to each one. We are told these investments are ‘independent’ and ‘identically distributed’. What does that mean?

‘Independent’ means that the performance of one investment doesn’t directly influence the performance of another. Think of it like flipping coins. If you flip a coin and get heads, it doesn’t change the odds of getting heads or tails on the next coin flip. In our portfolio context, imagine you invest in a tech company and a completely unrelated farming company. The success or failure of the tech company, assuming they are truly independent, shouldn’t automatically cause the farming company to succeed or fail. Their risks are separate.

‘Identically distributed’ means that each investment, on its own, has a similar level of inherent risk and potential return. Imagine each flower in our garden has a roughly similar chance of facing disease or thriving, and a similar potential to blossom. In investment terms, perhaps each stock you choose is from a company of similar size and industry risk profile, even if they are in different sectors for independence.

So, what happens to the overall volatility of our portfolio as we keep adding more and more of these independent, identically distributed investments, while keeping the portfolio equally weighted? Here is the fascinating part: the portfolio’s volatility decreases. This is a beautiful demonstration of diversification in action.

Think of it this way. If you only invested in one single, risky asset, your portfolio’s volatility would be exactly the same as the volatility of that single asset. It would be fully exposed to all the ups and downs of that one investment.

But as you add a second, independent, identically distributed asset, and then a third, and then many more, something interesting starts to happen. When one investment performs poorly in a given period, another independent investment might perform well, or at least not as poorly. These variations start to offset each other. It’s like having some flowers in your garden that are thriving even while others are temporarily wilting.

As you add more and more of these independent risks, the portfolio’s overall volatility starts to smooth out. The extreme swings become less pronounced. It’s like averaging many independent coin flips. While any single flip is either heads or tails, the average outcome over a large number of flips gets closer and closer to 50% heads and 50% tails, becoming much more predictable.

However, it’s crucial to understand that the portfolio volatility doesn’t magically disappear entirely, even as you add a huge number of independent assets. Why? Because each individual asset still has its own inherent risk. Even in a large portfolio of independent risks, there is still some level of ‘background noise’ or individual asset volatility that remains. It’s like even in a very diverse garden, there will still be some degree of natural variation in the health and growth of individual plants due to their own unique circumstances.

So, as the number of independent, identically distributed assets in an equally weighted portfolio increases, the portfolio’s volatility decreases, but it doesn’t decrease to zero. It approaches a lower limit, which is related to the average risk of the individual assets, but significantly reduced from the risk of holding just a single asset. This is the power of diversification: spreading your investments across many independent sources of risk to create a smoother, less volatile overall investment journey.