Financial Goal Planning – The traditional approach

Investing for a financial goal is perhaps one of the most common forms of investing. Go to any Financial Planner’s website and you would find goal planning at the top of the list of services they provide.

However, traditional approach to goal planning, and more specifically, the traditional approach to portfolio selection for a goal is not really optimal as we will explore in this blog.

But first, let’s quickly define financial goals.

A strict definition of “goal”

For financial goal planning, first, we need to have a strict definition of a goal. By strict, we mean that only those investment objectives that meet a certain set of pre-defined criteria can be classified as goals.

Here is how we chose to “strictly” define a goal:

• A goal must have an explicitly defined horizon.
• A goal must have a target – the amount of wealth needed at the horizon. This can be explicitly defined or derived.

Once the above 2 parameters are defined, we need to derive 3 variables – the starting wealth (let’s call it initial lumpsum), future injections (let’s call it SIP) and the required annualized rate of return (let’s call it irr) that is needed to achieve the goal.

In order to uniquely arrive at a realistic number for the above 3 variables, we need to fix 2 of them and calculate the third.

Note that future injections need not be limited to monthly SIPs. They could be anything – a fixed amount quarterly (or any frequency), sporadic injections at irregular frequencies or a fixed monthly SIP that grows annually.

Planners can use 2 approaches:

1. Let the investor define the initial lumpsum and future injections and then derive the required return and then recommend a plan or
2. Let the investor define the initial lumpsum, assume a realistic required return and then calculate the required future injections.

Both approaches can involve a back-and-forth discussion between the investor and the planner so that, eventually, they arrive at an amount that the investor can feasibly invest and a required rate that can be realistically achieved. If that does not happen, planners must go back to the drawing board and adjust the original 2 parameters.

Investment objective in goal planning

Why do we need to have such a strict definition of financial goals? Why can’t a general long-term wealth creation be a financial goal? It’s because investment objectives are different and hence, portfolio selection approach becomes different.

It is very important to understand that investment objective in goal planning is completely different from investment objective in general long-term wealth creation.

Note that long-term wealth creation is not a “goal” as per our strict definition. It doesn’t have a strictly defined horizon (in most cases) or a target level of wealth. Long-term wealth creation for retirement with a defined retirement date and a defined corpus does indeed become a financial goal.

What’s the investment objective for long-term wealth creation? It’s something like – “compound my money at a certain level of risk”.

For goals, the investment objective changes to “maximize the probability of achieving the goal”. In other words, maximize the probability that the final wealth at horizon is greater than or equal to the defined target wealth.

Why bother with investment objectives? Aren’t the 2 objectives similar? No, they are not. They require different portfolio construction approach, as we will see later in this blog.

Traditional approach to portfolio construction

Let’s take a concrete example. We will continue to work with this example throughout this series on Goal Planning.

For the choice of portfolios, we restrict ourselves to only 2 assets – risky asset represented by exposure to Nifty 50 Index through ETF and risk-free asset represented by exposure to a Liquid fund.

Our choice of portfolio turns out to be not very restrictive as it is aligned with the notion of CAPM which states that market (in our case Nifty 50) is the most optimal portfolio, and all efficient portfolios are a linear combinations of market portfolio and risk-free asset. Theoretically, we have simply restricted ourselves to CAPM efficient portfolios.

Here is a stylised version of how a typical conversation between an investor and the financial planner (FP) could go:

Investor: I am 30 and I intend to buy a house at the age of 40.

FP: Ok. You have any rough idea of how much your house costs today?

Investor: Roughly Rs 1 cr.

FP: Sounds good. Let’s assume that real estate prices increase by 6% every year. You would need roughly Rs 1.79 cr to buy your house in 10 years’ time. Can you invest something right now for this goal?

Investor: Yes. Rs 1 lac.

FP: Great. How much risk are you willing to take?

Investor: I am not very aggressive. Maybe moderate levels of risk.

FP: Ok. Then we can target a required return of 9%. You will need to invest Rs 91,000 every month or you can start with a monthly SIP of Rs 76,000 and grow it by 5% every year or you can start with a monthly SIP of Rs 62,000 and grow it by 10% every year.

Investor: I think I can start with Rs 76,000 and grow it by 5% every year.

FP: Brilliant! We will invest in a portfolio of 40% NIFTYBEES ETF (that tracks Nifty 50 index) and 60% HDFC Liquid fund. This portfolio, if held for 10 years, has an expected return of roughly 9.8% and a volatility of 5.1%. This portfolio is aligned with your risk profile as well.

Investor: All right then. Let’s get started!

Mind you, we are dealing with a pretty good financial planner here. But he has made 2 mistakes.

First, he has not used probabilities of achieving the goal to arrive at the required return. Instead, he has used investor’s risk tolerance. In our example, it works out to be fine because 9% is a reasonable target to have.

However, suppose that the investor would have said that he is aggressive and willing to take on risk. Our financial planner would have then suggested a 14% expected return portfolio (100% Nifty 50 index) and said that you only need to invest Rs 58,000. On the face of it, investor would be happy. He now only needs to invest Rs 58,000 instead of Rs 76,000. But it turns out that the chances of achieving the goal is barely 51%.

To calculate the probabilities, we have used a technique called historical bootstrapping to simulate 1000 possible 10-year paths of Nifty 50 and ran the portfolio for each path. We have used a deterministic 4% annual return from liquid fund and not assumed any taxes or transaction costs. Probability is calculated as the number of paths in which portfolio’s final value is greater than the target value divided by 1000.

Second mistake is to use “Expected return” as the portfolio selection criteria. Returning to our example, our planner has recommended a portfolio with an expected return of 9.8%. With this portfolio, the chance of achieving the goal is barely 53%.

Mathematically, this makes sense since your required return is same as expected return. Remember, expected return is the “average” return which implies that 50% of return scenarios could be below this expected return (and even that is not guaranteed in case of skewed distribution which is generally the case). The chart below shows the probability of achieving the goal for different portfolios:

Another interesting chart shows the probability of achieving the goal for different levels of required return and horizon. Y axis is required return and X axis is the horizon. Probabilities shown are for the highest probability portfolio for that level of required return and horizon.

Note that chart 1 and chart 2 have been created using different starting assumptions – sip and no sip and hence the numbers, although similar directionally, will not match exactly.

There are a few interesting observations:

1. The riskiest portfolio (100% Nifty 50) has the highest probability of achieving the goal.
2. Marginal contribution of risk is decreasing. As you move from a 30:40 portfolio to a 40:60 portfolio, there is a 11.9% jump in probability. However, as you move from 90:10 portfolio to 100:0 portfolio, the probability increases by just 0.8%.
3. Probabilities decrease as we move from lower level of required returns to higher level. This is expected.
4. Another interesting observation is that at lower level of returns (up to 13%), probabilities increase as we increase the horizon. However, for higher levels (15% onwards), probabilities decrease as we increase the horizon. It is no surprise that cutoff of 14% is the expected return of Nifty 50.

These observations can help us in selecting portfolios for financial goals. Risk, as defined by volatility, cannot be the primary deciding factor in portfolio selection.

Goal planning and eventual portfolio selection becomes an intricate exercise in probability management. Probabilities themselves are a function of required return and horizon.

General rule of thumb could be:

1. Given a required return and the horizon, you should select a portfolio that has a projected probability of over 70% of achieving the goal.
2. If no portfolio fits the bill, you should go back and rework the goal expectations to bring down the required return or increase the horizon. For example, at a required return of 14%, even the best portfolio had a 51% probability. Clearly, 14% is not the right target for planning this goal.
3. Risk aversion should only enter in the second stage to exploit the decreasing marginal contribution of risk. In our example, for a risk averse investor, we can settle for a 70:30 portfolio instead of a 100:0 portfolio.
4. At the same time, investors should be communicated about the expected volatility levels in the portfolio and if the investor is not comfortable with that, planner should go back to point 2.

So far in our analysis, we have assumed that the starting portfolio remains the same throughout the goal horizon. In our example, suppose we start with 70:30 portfolio (that has a starting probability of 70.8%), then we stick with this for 10 years. This is a static approach to goal planning.

Clearly, this cannot be optimal. Suppose we enter a bear market for 2 years and after 2 years, the required return of achieving the goal becomes 12% (from 9%). We will need to correct the course and select a different portfolio. This is a dynamic approach to goal planning. We discuss this approach in more detail in our next blog.