Adaptive Asset Allocation : Case Study

Harnessing Targeted Returns, Volatility, and Correlation for Optimal Investment Strategies

Three Key Ingredients for Asset Allocation

Targeted Returns: Aiming for Growth

Every investor wants their money to grow. Expected returns represent the average profit you anticipate from your investments over a specific timeframe. This is the primary goal of any investment strategy: to generate a positive return on investment.

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Volatility: The Risk Factor

The road to returns isn’t always smooth. Volatility measures the price fluctuations of an investment. High volatility means significant swings, both up and down. This volatility can disrupt your return goals, especially if it makes you panic and sell during a downturn. Understanding and managing volatility is crucial for maintaining a steady investment strategy.

Correlation: The Diversification Ally

To manage volatility, correlation comes into play. It signifies how investments move together. By understanding correlation, you can diversify your portfolio. Imagine having stocks (apples) and bonds (oranges). Ideally, they’d have a negative correlation. If stocks fall (bad for apples), bonds might rise (good for oranges), balancing your portfolio and reducing risk.

In essence, you chase returns but face volatility as a hurdle. Correlation helps you manage this risk by strategically diversifying with assets that move differently. This way, even if one asset class experiences a downturn, another with a negative correlation might rise, potentially offsetting losses and keeping you on track towards your return goals.

Now that we’ve unpacked the key ingredients of asset allocation — expected returns, volatility, and correlation — let’s discuss how portfolio optimization helps us leverage them effectively. Imagine you’re a chef creating a delicious meal. You have various ingredients (asset classes) with different flavors (risk-return profiles). Asset allocation is like choosing the right ingredients, but portfolio optimization is like mastering the recipe. It helps you combine these ingredients in the optimal proportions to achieve your desired outcome — a delicious dish (a well-balanced portfolio) that meets your taste (risk tolerance) and hunger (financial goals). By understanding how portfolio optimization works, Indian investors can create personalised investment strategies that navigate market volatility and target their long-term financial aspirations.

The Objective of Portfolio Optimization

One of the most important axioms in finance is that the best estimate of tomorrow’s value is today’s value. This prompts the question: if we can measure the value of these variables today (or over the recent past), and they are better estimates over the near-term than long-term average values, why not construct portfolios based on this current information? That is, why wouldn’t we choose for our portfolios to adapt over time based on observed current conditions?

It is worth noting that the overall objective of asset allocation is to deliver the highest returns per unit of risk, where risk is usually defined in terms of volatility. In finance, the ratio of a portfolio’s return to its volatility is called the Sharpe ratio, and this is one of the most fundamental units in finance . You may wonder why we don’t just focus on returns. Well, one reason is that higher risk portfolios are much more difficult to stick with. That’s because more volatile portfolios are generally more vulnerable to periods of large losses. For example, we observed that stocks have a higher long-term return than bonds, and higher accompanying volatility. We also know that stocks are vulnerable to periods of extreme losses, in the neighbourhood of 50–90% during the most ferocious bear markets. In contrast, bonds have lower returns and lower volatility, and thus we observe much more tolerable losses during bond bear markets. But at root, higher volatility simply implies that the actual returns that an investor can expect to realise over a finite investment horizon lie in a larger range. This cuts both ways; an optimistic investor might point out that stocks have the potential to ‘shoot the lights out’ in a way that bonds will never do. While this may be the case, most investors are not investing in hopes of a lottery payoff. Rather, most investors hope to earn good returns, but realise they can’t easily endure a highly unlucky outcome, with large losses that last for many months.

Technically, the Sharpe ratio measures the ratio of excess returns to volatility, where returns are measured in excess of the risk-free rate. However, for simplicity, all Sharpe ratios in this paper are simple ratios of returns / volatility.

It’s critical to understand that volatility is just as important to the investment equation as returns, because volatility describes the range of returns that might be expected over a finite investment horizon.

In fact, the volatility side of the coin may be even more important than the return component for typical investors with 3–5 year emotional investment horizons (that’s probably you).

In the next section, we will explore a variety of methods for constructing portfolios, which adapt to observed changes in expected market returns, risk, and correlation. You will see that by observing and adapting to current market conditions it is possible to construct dynamic portfolios, which have the potential to deliver higher returns with less risk.

Introducing Adaptive Asset Allocation

Adaptive asset allocation is a strategy that adjusts the composition of a portfolio based on current market conditions. By observing and adapting to changes in expected market returns, risk, and correlation, it is possible to construct dynamic portfolios that have the potential to deliver higher returns with less risk.

To demonstrate the advantage of adaptive asset allocation, let’s consider a portfolio consisting of five major asset classes:

• MON100 (NASDAQ)
• NIFTYBEES (Nifty 50)
• JUNIORBEES (Nifty Next 50)
• GOLDBEES (Gold)
• ASBL Liquid Fund (Debt)

Case Study: Portfolio Performance

1. Naïve Buy & Hold Strategy : First, consider a naïve investor, with no knowledge of expected relative asset class performance, risk, or correlation information. Let’s assume he would simple Buy & Hold NIFTYBEES since 1–07–2014 and would have experienced the portfolio growth profile described below

• CAGR: 12.73%
• Max Drawdown: -28.81%
• Volatility: 15.82%
• Sharpe Ratio: 0.80

Before we move on, let’s review how to interpret the chart and data table from Exhibit 1. The top chart shows the growth of 100 invested in the strategy on July 1st, 2014 through May 2024, where it seems to have grown to about 329 Rs. It offers a visual representation of the growth in the portfolio through time, which is summarized in the table below. For example, the compound returns, which took the portfolio from 100 ten years ago to 329 today, equates to 12.7% per year. The top chart is also informative because you can see the path the portfolio took to get from 100 to 329, which included a big dip about 28% of the way along in 2020. We take these dips very seriously, so below the growth chart we plot the drawdowns through time as a percentage of the portfolio’s drop from its all-time peak. From visual inspection, you can see that the portfolio lost about 28% of its value in the 2020 COVID crash. This is confirmed by glancing at the Max Drawdown data in the table, where we learn that in fact the maximum drawdown was a drop of 28% from peak to trough. Please also note the portfolio volatility and simple Sharpe ratio. The volatility of the portfolio over the entire period averaged 15.8%, which means the Sharpe ratio was 12.7% / 15.8% = 0.8.

2. Equal Allocation Among All Assets : For our next study, let’s assume that an investor believes he has some knowledge of various assets available, but no knowledge of volatility or correlations. So as a rational investor he allocates equally among all the 5 assets available.What happens then ? Chart below gives the answer.

• CAGR: 14.11%
• Max Drawdown: -13.17%
• Volatility: 10.34%
• Sharpe Ratio: 1.37

By allocating to each asset in the portfolio equally, the return delivered per unit of risk (Sharpe ratio) increases from 0.80 to 1.37 relative to the Buy & Hold NIFTY portfolio . Of course, this improvement is mostly a function of less overall portfolio volatility. Not surprisingly, less volatility also means lower maximum drawdowns (-13% vs. -28% for NIFTY Buy&Hold).

We have seen that by allocating across assets , we have played with great team effort. Now let’s put our offensive team on the field : Momentum

3. Momentum Strategy : We ranked the 5 assets based on their performance over the past year and selected the top 2 to build the sample portfolio showcased below

• CAGR: 13.57%
• Max Drawdown: -25.08%
• Volatility: 13.22%
• Sharpe Ratio: 1.03

The returns did not improve significantly.

Wait , What just happened ? Momentum was supposed to work right ? Then why didn’t the returns improve ?

The answer lies in Correlation. Our Universe of 5 Assets had below Correlation among themselves. Take a look the correlation between assets played a crucial role in the performance. High correlation between assets can reduce the effectiveness of a momentum strategy. Take a look.

As you can see The table above shows the correlation coefficients between different assets. A value close to 1 indicates strong positive correlation (move together), close to -1 indicates strong negative correlation (move opposite), and close to 0 indicates weak correlation (little connection).

• High Correlation: Looking at the table, several pairs have high correlations (e.g., NIFTYBEES and JUNIORBEES at 0.87). This suggests these assets tend to move in the same direction.
• Diversification: For a well-diversified portfolio, you generally want assets with lower correlations. This helps spread risk because if one asset class performs poorly, others might not be as affected.

Potential Removal Candidate:

• NIFTYBEES or JUNIORBEES: Since they have a high positive correlation (0.87), their movements are quite similar. Removing one might not significantly impact diversification.

Let’s see what happens when we remove JUNIORBEES and do the same exercise

4. Removing Highly Correlated Assets

• CAGR: 17.42%
• Max Drawdown: -16.78%
• Volatility: 12.54%
• Sharpe Ratio: 1.39

Voila, By removing JUNIORBEES and focusing on less correlated assets, returns improved significantly (17.42% as compared to 13.57% ) with lesser volatility (12.54% as compared to 13.22%).

Remember that diversification has the effect of lowering the risk of a portfolio because some assets in the portfolio are ‘zigging’ while others are ‘zagging’. Importantly, two assets can have a low correlation, and therefore effectively diversify each other, even while both assets are moving in the same average direction. That is, two assets can be rising in price on average, but be negatively correlated.

To understand why, consider the chart below, which shows two securities with positive return trajectories, but that move in opposite directions at each period. As a result, the two securities have perfect negative correlation, while the portfolio of the two securities moves in a straight line, up and to the right. In this way, two risky assets with equal volatility and perfect negative correlation can be combined to form a portfolio with zero volatility and a positive return

The best way to visualise zig-zag-ness of two assets is by plotting their rolling 1 year correlation.

As you can see correlation between GOLDBEES and NIFTYBEES oscillates around 0 and can be termed as weak suggesting that the prices of gold and Nifty tend to have a low correlation, meaning their movements are not strongly tied together.

The opposite is also true , if you have two assets which move together in unison they will not necessarily add any benefits to your portfolio.

In the chart below you can see the rolling 1 year correlations between nIFTYBEES and JUNIORBEES are very high indicating strong movements together.

5. Volatility-Adjusted Portfolio : So far, we have observed a step-by-step improvement as we introduced methods to better diversify portfolio and harness the momentum factor. We have also noticed that having too many offensive players in a team is not good either. Our one missing ingredient to make it a formidable team is defence i.e. volatility. We have not taken any steps to account for different asset volatility as we construct portfolios.Let’s do that

• CAGR: 16.60%
• Max Drawdown: -8.91%
• Volatility: 10.47%
• Sharpe Ratio: 1.58

Now, we have improved our Returns per unit of Risk from 1.39 to 1.58 by playing great defence along with great offence. Look at maximum drawdowns as well they are at -9% which is a massive reduction from where we started at -29% (NIFTY Buy & Hold)

But what do we do here exactly ?

We simply sized each asset in the portfolio so that it is expected to contribute the same amount of (nominal) risk. Of course, this improvement is mostly a function of less overall portfolio risk, as the returns are very similar (16.6% vs. 17.4% for equal weight). Not surprisingly, less volatility also means more consistent returns and lower maximum drawdowns. And we get all of this benefit simply from preventing the lunatics (Assets) from running the asylum (portfolio).Adjusting for different asset volatility improved the returns per unit of risk further. This strategy resulted in more consistent returns and lower maximum drawdowns.

Conclusion

Through adaptive asset allocation, investors can construct dynamic portfolios that adapt to changing market conditions, aiming for higher returns with less risk. By leveraging expected returns, managing volatility, and understanding correlation, you can create personalized investment strategies that navigate market volatility and target long-term financial goals.

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**Disclaimer:** We are not SEBI registered advisors. Any content shared on or through our digital media channels is for information and education purposes only and should not be treated as investment or trading advice. Please do your own analysis or take independent professional financial advice before making any investments based on your own personal circumstances. Investment in securities is subject to market risks; please carry out your due diligence before investing. And last but not least, past performance is not indicative of future returns.