QUANTITATIVE GOAL-BASED FINANCIAL ADVICE
By: Anupreet Choudhary
Tags: Data Science, Stock Market, Financial Planning, Finance, Financial Advisor

Goal-based financial advice is usually based on investor’s risk averseness and the current market condition (hypothesized by fundamental and market parameters). The asset allocation models use these parameters to switch between equity and other asset classes. This approach misses the time-horizon element of the goal. An investor, although risk-friendly, can’t fulfill his short-term financial goal by taking a risk exposure to equity markets. As per the capital asset pricing model (CAPM), an investor shall earn a risk-premium in the long-run for the risk-exposure (beta) she has taken now, hence the idea of time-horizon is important.

This article holistically approaches the goal-based advisory problem by including the time horizon element into the models. These advisory models are based on horizon-dependent return’s distribution and it gives more weightage to downside risk to cater to capital protection.

Further, the article lays a foundation for portfolio management specific to the equity asset class. It introduces a framework for managing portfolios pertaining to asset-allocation.

Introduction

If you have ever asked someone to advise you on your wealth and financial planning, you must have likely encountered a standard ‘risk-assessment’ questionnaire. This questionnaire is usually used to define broader allocation limits on various assets (debt & equity in most cases). These limits are further refined with a ‘dynamic allocation’ framework, which usually captures the relative valuation of asset classes.

The problems with this framework are as follows:

1. The risk-assessment questionnaire only focuses on investor’s risk-taking ability but ignores the investor’s goal timeline. An investor might be a risk-taker by behavior but would not fulfill a near-term goal by buying more risky assets. In other words, the probability of losing money is more in near-term, hence no matter how risk-taking an investor is, if her goal is a near-term goal, she would fail to achieve her goal if we ignore the time-horizon element in our asset allocation models

2. Asset allocation models have two broad levels — strategic asset allocation (broadly defines the limits) and dynamic asset allocation (broadly caters to the current market situation). A common practice in the industry is to use valuation ratios, typically price-to-book, price-to-earnings, etc., of a broad market index, to assess the cheapness or expensiveness of equity asset class. Basis of this assessment, the dynamic allocation models allocate capital to various asset classes. The fundamental issue in this approach is that in case of tail events (financial crisis, epidemics, etc.) every asset class shall under-perform despite having a low/high valuation for that period

3. One important consideration in all asset allocation models is that they don’t account for withdrawal patterns. The investor’s withdrawal pattern is a function of goal type and investor behavior. A goal like buying a house (where all the money shall be withdrawn in a lump sum) is completely different from a goal like planning for retirement.

4. Lastly, many asset allocation models ignore the risk element while modeling. They assume that the world revolves around averages, but they ignore the ‘spread’ around the average

Typically, asset allocation advice should be backed with a solid base of underlying assets. Imagine that, for a client, you come up with 60/40 equity/debt asset allocation for a goal. And in equity allocation, you come up with a list of mutual funds for diversification. This is fundamentally a correct approach, but since the very structure of a long-only mutual fund (or any equity product for that matter) is opaque, you would not have too much control over the risk and return of a particular asset class.

This becomes important because most of the advice in the industry is based on Nobel Prize-winning Markowitz’s mean-variance framework. The important consideration in Markowitz’s framework is to forecast the risk and return of different asset classes. The mean-variance optimization technique is very sensitive to inputs, hence accurate forecast is required, which is difficult for products like mutual funds. Also, rebalancing using mutual fund products will be costly.

Given the above issues, the investor should have such underlying assets on which she has control. In this article, we shall discuss the strategic asset allocation part which broadly sets asset allocation limits as per investor’s goals.

In the later series of articles, we shall discuss other elements of goal-based advisory like portfolio management for each asset class. Figure 1 describes the entire flow chart. For any goal, we shall start with a broad allocation limit (giving more weightage to downside risk) and then refine it further by considering each investment model.

Figure 1: Horizon based allocation glide frontier: Allocation glide path (HAGF) takes the investor’s goal to come up with an optimal risk-based allocation. Metamodels allocate capital between different Investment Models (IM)

Financial goals and investment horizon

First, let’s understand how investors assess their financial needs:

Investors have goals

2. Goals can be short-term (like a vacation) or long-term (like planning for retirement)

3. Goals should be independent (vacation goal should not have any impact on retirement goal)

4. Investors hate it if their goals are not achieved

5. Sometimes investors are clueless about their goals

6. Each goal has a final liquidation assumption

7. Investors can have their risk preferences

8. Investors have few sources of income hence they prioritize the goals with different horizons (like they can choose to buy a car over going for a vacation)

As an investment advisor, we should understand the investor’s goal and see how they can achieve it without risking their capital. Once we have goals in place, we should look at the investment horizon and withdrawal pattern for each goal and build an allocation glide path for each goal. Each goal is independent and serves a different purpose (although statistically, they can have a high correlation). Hence, each goal should be viewed differently. Figure 2 explains this process.

Figure 2: Financial goals are independent: Each goal is different and independent. Each goal will have a different allocation glide path. The capital allocated to each goal shall depend on the investor’s goal prioritization order. The capital allocated can increase or decrease over time, ideally should be at a fixed rate.

A goal like buying a house would require sudden withdrawal at the end of the period, while a goal like income for retirement will have a staggered withdrawal pattern. Table 2 summarizes some of the investment goals mapped with their horizon and withdrawal patterns.

Time horizon and withdrawal pattern depends on the investor’s financial need

With the information on time-horizon and withdrawal patterns, we can determine the optimal level of risk for a given time horizon based on different possible outcomes. The process of defining risk levels is explained in the next section.

Balancing risk with time

Let’s consider you have Rs 1,00,000 to invest for a goal with sudden withdrawal at the end of the period. The investment can have a different possible outcome for different time horizons. The figure below plots different levels of outcomes (I will discuss how I calculate different levels of outcomes in a while)

Figure 3A: Equity investment value for different percentile levels: BSE Sensex Index is used as a proxy for equity investment. Period of analysis: Jan 2, 1980, to May 7th, 2020

The 3-year expected value for 100% equity portfolio is Rs 1,38,676 (50th percentile) but the range of possible outcomes varies from Rs 3,18,927 (95th percentile, 47% CAGR) to Rs 87,075 (5th percentile, -5% CAGR). This is a great example to explain how stocks can have a huge potential for upside but at the same time carry some risk element.

If we plot this till 10 years, it’s less likely to get negative returns. For 10 years, even the 5th percentile will yield a portfolio value of Rs 1,33,113 (3% CAGR).

Figure 3B: Equity investment value for different percentile levels: BSE Sensex Index is used as a proxy for equity investment. Period of analysis: Jan 2, 1980, to May 7th, 2020

All these observations are in-line with various asset pricing models like the capital asset pricing model (CAPM). In the long-run, investors earn a risk premium for the risk exposure they have taken in the short-term.

Figure 4: Equity investment value for different percentile levels from 5th to 50th percentile: BSE Sensex Index is used as a proxy for equity investment.

How outcome levels are derived?

The outcome levels are derived from a distribution of expected returns of the underlying portfolios. For a proxy of expected returns, we can use an index that truly represents the underlying portfolios. For this article, I have taken S&P BSE Sensex (I will refer it as Sensex in the remaining part of this article) and CRISIL Composite Bond Fund Index as my proxies and have studied their distribution of returns over time to calculate outcome levels. In reality, the distribution should reflect the risk and return parameters of the underlying portfolios.

Coming back to my proxies, the stock market price data is very heterogeneous. The parameters of the distribution of returns changes with the horizon. Figure 5 gives you a comparison of returns distribution for different periods. One observation that we can draw from it is that the short-period distribution has higher volatility (has a wider distribution) as compared to long-period distribution. Also, long-period distribution is smoother and close to a normal distribution (see figure 6). This explains well how risk and time interact with each other.

Figure 5: Returns distribution for different periods: Period of analysis: Jan 2, 1980, to May 7th, 2020

Figure 6A: Q-Q plots for 1-year returns

Figure 6: Q-Q plots for 10-year returns

Comparing it with the fixed income counterpart, the distribution for Sensex is much wider for any period. This explains that equity investments are risky, and investors earn risk-premium for taking that risk.

Figure 7: 10-year returns distribution for debt and equity

Constructing Horizon based Allocation Glide Frontier (HAGF)

In the previous section, we have defined the relationship between return, risk, and time. Now we know how different time horizons have a different distribution. We can use these distributions to make an appropriate recommendation for stock and bond allocation.

We will take all possible stocks allocation (from 0% to 100%) for a given equity percentile level.

To explain this concept, consider an example below:

Here we see the 20th percentile outcome for every stock allocation over a 20-year investment horizon. We will consider the 20th percentile outcome as the “bad case”. With a shorter horizon, you can see that the model shows 100% debt allocation. While for longer horizon 100% equity allocation is the best choice.

Now let’s see the best allocation in each period. It’s nothing but the top part of this graph. I’ll call this as a percentile glide path. You can see that after 7years, at the 20th percentile outcome, 100% equity allocation is advisable (since it’s the best option available). Similarly, below 7years 100% debt allocation is advisable.

Figure 8: Percentile glide path for the 20th percentile equity and 50th percentile debt

Another way to view this percentile glide path is to change the value of the y-axis from absolute values to stock allocation %. This graph will tell you how the allocation must have performed best for a given period in a ‘bad’ scenario (we consider the 20th percentile as the ‘bad’ scenario).

Figure 9: Percentile glide path for the 20th percentile equity and 50th percentile debt in terms of equity allocation percentage

This is the case when we have taken the 20th percentile for equity outcome and 50th percentile for debt allocation. We can be more conservative and vary the percentiles for debt outcomes (from 5th percentile to 50th percentile) for each equity percentile as well. If we do so, we will have 46 different percentile glide paths. We can then take their average to come up with a final percentile glide path for a percentile of equity outcome. This is shown in figure 10

Figure 10: Percentile glide path for the 20th percentile equity and 5th — 50th percentile debt in terms of equity allocation percentage

Now, we can use the same concept to make percentile glide path for all the percentiles, from the 5th percentile (close to the worst case) to the 50th percentile (expected outcome). Remember that any percentile glide path over the 50th percentile will show 100% equity allocation in all periods. Our aim here is to provide our investor with a seamless experience of meeting her goal. Hence, we should give more importance to downside risk as compared to the upside potential. To do that, we will take an average (we can change this as well for a different level of risk tolerance) of all percentile glide paths from the 5th percentile to the 50th percentile. We call this as ‘HAGF’ (pronounced as “hough”, short form for Horizon-based Allocation Glide Frontier).

Figure 11: Horizon-based Allocation Glide Frontier — Balanced investor

You can see that if your goal is a long-term goal, 100% equity allocation is advisable. As you approach your goal date, HAGF will reduce your equity allocation and increase your debt allocation.

Figure 12: Horizon-based Allocation Glide Frontier — Balanced investor

Including investor’s risk preference

In the previous section, we have taken an average of various percentile glide path to come up with a HAGH. We can also take a weighted average of percentile glide path depending on the investor’s risk tolerance.

Figure 13A: Weights — Aggressive investor

Figure 13B: Weights — Balanced investor

Figure 13C: Weights — Conservative investor

Figure 14 shows weights given to different percentile glide paths for different risk preferences.

Figure 14: Weights — Horizon-based Allocation Glide Frontier for different investors

One thing to note here is that the risk preference also depends on the goal’s type. For example, for major purchase goals, the recommended HAGH takes a more conservative path than a recommended HAGH for a retirement goal. This is because we expect the investor will fully liquidate her investment at the intended date and will need the full balance. Retirement, on the other hand, would have a staggered liquidity preference.

We can use this framework to decide a reasonable range of deviation for different risk preferences.

Closing thoughts

An allocation cannot be optimal if the investor is not comfortable committing to it in both good markets and bad ones. Including the time-horizon element into the models lists out the risk of an investment. Remember that 100% equity allocation is only advisable if the investors have a long-term view. To ensure that investors understand and feel comfortable with the short term risk in their portfolios, we should look at both extremely good and extremely poor return scenarios