# Risk in Portfolio Construction

In our previous report, we discussed how practitioners typically measure investment risk. We also noted how there are ways to reduce risks in a portfolio, such as ‘diversification,’ which can help reduce volatility. Today, we further analyze risk in the context of portfolio construction.

## Uncorrelated assets reduce risk

In practice, two stocks (or assets generally) rarely move up and down at exactly the same time. Because of that, putting them together in a portfolio usually reduces the risk of the overall portfolio. Correlation is a statistical measure that calculates whether the direction of returns across two or more assets is related or offsetting (as we show in Chart 1 below).

We show how that works in the three example portfolios below where:

1. Stock PC is perfectly correlated (moves in sync) to Stock AA: Here, blending the two stocks together doesn’t reduce portfolio volatility (grey area).
2. Stock UC is uncorrelated (moves are not related) to Stock AA: Here, blending the two stocks together reduces portfolio volatility a little.
3. Stock NC is negatively correlated (moves in opposite directions) to Stock AA: Here, blending the two stocks together eliminates portfolio volatility (the grey portfolio value remains unchanged despite moves in each asset.

Chart 1: How stocks with different daily returns (correlation) dampen portfolio volatility

Correlation ranges between -1 (perfectly negative) and +1 (perfectively positive). In the example above, the correlation of stock UC and AA is equal to 0, so we say their returns are “uncorrelated.”

We see in the data above that combining stocks with different correlations can produce different levels of portfolio risk (being the variability in their daily returns).

For example, Chart 2 below shows an example of five stocks (A, B, C, D, E). Each stock has 20% single security risk (grey bars, left side). The right side shows the correlation of each stock to A (e.g. Stock B has a correlation of 1, whereas Stock E has a correlation of -0.50.

The blue bars reflect the “portfolio” risk when we combine Stocks B, C, D, and E with Stock A. Note that the portfolio of Stock B + Stock A has the same portfolio risk as Stock B or Stock A alone (due to the correlation being 1). However, a portfolio such as Stock E + Stock A is able to reduce portfolio risk (since the correlation between Stock E and Stock A is negative). This reduction in portfolio risk is generally referred to as the benefit of portfolio diversification.

Chart 2: How different correlations reduce portfolio risk

Of course, the concept above can also be applied to portfolios with many different assets.

## What is diversification?

When it comes to portfolio construction, investors try to ‘diversify’ their portfolios by blending dozens or hundreds of different assets into their portfolio. This takes advantage of how differently correlated assets can reduce portfolio risks, or even the size of portfolio drawdowns, sometimes without reducing returns.

## Components of total portfolio risk

However, not all types of portfolio risk can be diversified away. That’s because there are generally two types of portfolio risk:

• Diversifiable (also known as unsystematic, idiosyncratic, or company-specific)is related specifically to a company. For example, if a company misses on earnings, or a CEO departs, these can have an immediate and more direct impact on just that company’s valuation.

• Non-Diversifiable (also known as systematic) is related to the broader market. For example, global recessions, the COVID-19 pandemic or central banks raising interest rates may have some impact on all companies regardless of their specific sizes or sectors.

Chart 3: Two types of long-only portfolio risk

Of course, there are ways to reduce non-diversifiable (or market) risks, but it usually involves hedging using financial products including but not limited to short futures, short ETFs or options, which can reduce expected upside returns from holding a long-only portfolio.

## Does diversification reduce risks consistently?

In reality, a professional investor typically has thousands of stocks (or assets) to choose from – each with different levels of correlation.

This raises an interesting question: If you simply add more stocks to a portfolio, what happens to the benefits of portfolio diversification?

Portfolio theory teaches us that only company-specific risk can be ‘diversified’ away by adding more stocks to a portfolio. This seems to suggest that there are marginally decreasing benefits (to risk) from incrementally adding more stocks (Chart 4).

Chart 4: Two types of portfolio risk

## How quickly does diversification work?

If we look at real data, we see that that’s exactly what happens.

In the chart below, we rebuild increasingly broader portfolios, taking the Top N (number) of stocks from the Nasdaq US 500 Large Cap™ Index (Nasdaq’s own benchmark for the top 500 U.S. large-cap stocks) and blending them at market weights (like we did in this study).

Each dot in Chart 5 represents a portfolio with the number of stocks inside the circle. We then compare that to the volatility of the whole 500-stock benchmark.

Chart 5: Diversifying U.S. large-cap portfolio risk

We see that a market cap-weighted portfolio of the top five stocks has higher risk than a portfolio of 10 stocks (around 25% vs 23% volatility). Eventually, portfolio risk (measured as the standard deviation of close-to-close returns) converges to the risk of the broader benchmark, which was around 19% annualized over the period.

## Diversification is important and achievable

We see from real data that diversification is important for investors. Sometimes, it can even reduce risks without reducing expected returns. That’s one reason why ETFs have become so popular. But here, we also show that creating a portfolio with close to benchmark risks is actually easier than you might think.

Importantly, an investor could get most of the benefits of diversification without owning the majority of stocks in the index.

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