The Five Numbers Framework
Investors want the highest return on their investment. Therefore, they blindly chase returns. Returns are typically expressed as a Compounded Annual Growth Rate (CAGR) figure. Higher CAGR means the investment has performed better over the period the CAGR was considered.
Typically, CAGR for investments is expressed in 1-month, 3-months, 6-months, 1 year, 3 years, and 5 years. All returns are annualized. Periods less than 1 year are expressed as a projection over 1 year.
Returns are Elusive
Returns do not describe the journey taken to achieve the figure by the investment manager.
These returns are historical and do not talk about other mathematical characteristics such as volatility, draw-downs, Sharpe ratio, betas, alpha, etc. These mathematical and statistical metrics help describe an investment more accurately.
However, investors do not care about these characteristics because:
- The metrics are difficult to understand and require sophistication.
- High return figures trigger a Confirmation Bias. This causes the investors to search only for evidence that supports choosing the investment with the higher returns.
- They assume that higher returns today will continue in the future.
In the end, investors typically end up taking risks with a poor understanding of how the returns came into being. Some of these risks are unsavory.
The Five Numbers Framework is intended to give investors a larger picture around the investment options in a figure they understand — Returns (CAGR).
The only sophistication the investors needs in this case is to be able to comprehend 5 return figures instead of one, and use simple rules around these figures.
Constructing the Five Numbers
The NIFTY50, India’s flagship large-cap index, has been around since 1995. It has been through at least 3 major cycles. Over a period of around 25 years, the CAGR of NIFTY50 has been 8.91% from 1-Jan-1995 to 1-Jul-2020.
By typical reporting standards the returns would have been as follows for periods ending on 1-Jul-2020:
- 1-month (annualized) — 106.61%
- 3-month (annualized) — 155.65%
- 6-month (annualized) — -26.76%
- 1 year — -12.07%
- 3 year — 3.08%
- 5 year — 4.29%
The 1-month and 3-month returns are staggeringly high because the market was recovering after hitting lows in March and April 2020. Longer period returns show a different picture.
However, neither of these return figures indicates an investor of how the future might shape up in the next 5 years. Returns may continue to stay low or reverse and perform very well. A longer historic perspective can help.
Rolling Returns
Rolling returns are annualized returns over multiple periods of the same time frame that the investors intend to invest for and offset by a set period. A rolling return period can begin at periodic intervals and the periods can overlap each other as well. Let us understand this with an example.
To consider the rolling returns of NIFTY50 over 5 year periods starting from 1995, we will offset each period by three months. These periods will have starting and ending dates which will look like below:
- Period 1: 1-Jan-1995 to 1-Jan-2000
- Period 2: 1-Apr-1995 to 1-Apr-2000
- Period 3: 1-Jul-1995 to 1-Jul-2000
- Period 4: 1-Sep-1995 to 1-Sep-2000
- …
And so on till the final period starting 1-Jul-2015 to 1-Jul-2020
83 rolling return periods are starting every 3 months from 1-Jan-1995 till 1-Jul-2020. Let us examine these returns. Plotting on a graph the 5-year rolling returns for each starting period would look like below.
The maximum return in any 5 year period is 41.03%. The minimum return is -3.06%. The average is 11.74%. This means if the investors were invested during any of these 5 year periods, they could have possibly got a return which would be anything between a whopping 41.03% to a dismal -3.06%.
Further, between any two consecutive 5 year periods, which are offset by 3 months each, the change in returns from one period to the next could be anything between -13.01% drop to 12.11% rise in comparison to the previous 5 year period.
These observations imply that not only is there a wide variety of outcomes of returns possible for the investors, but also that the recent past returns have no bearing on how the future returns will be.
This is an important expectation that needs to be set for the investors for them to make a better decision.
The Five Numbers
An investor’s expectation is set right when they are told that there is a range of outcomes possible in the next five years rather than the recent returns. This can be done in terms of returns themselves.
The maximum return out of these rolling period returns is The Best Case Scenario. The minimum is the Worse Case Scenario. These numbers are indicative that if the investors are extremely lucky or extremely unlucky, what should they expect. However, these are not the only possible returns the investors should look at.
The Best Case and the Worse Case Scenario returns are intended to introduce investors to the role of luck in investing. These numbers are not practical to be used for planning investments.
Of the 83 periods of rolling returns the median will express the most likely outcome with which the investors should plan their investments with. This is the Expected Return. In the case of NIFTY50, this is 9.75%. Interestingly, this is also nearer to the 25-year CAGR of 8.91% for the NIFTY50 index during the period from 1/Jan/1995 to 1/Jul/2020 in comparison to the average of 83 periods i.e. 11.74%.
Next, arrange the rolling returns in descending order. The maximum return or the Best Case Scenario will be on the top and the minimum or the Worse Case Scenario will be at the bottom. To get a realistic range of outcomes, we will use the Realistic Upside Returns and Realistic Downside Return metrics. The average of returns above the median is the Realistic Upside Returns. In the case of NIFTY50 for a period of 5 years from 1-Jan-1995 to 1-Jul-2020, this is 18.61%. Correspondingly, the average of returns below the median is the Realistic Downside Return. In this case, it is 4.83%.
In the case of NIFTY50 the table for the Five Numbers will be as follows:
Return Metric | Returns |Expectation
- Best Case Scenario | 41.03% | Very lucky outcome
- Realistic Upside Return | 18.61% | Realistic good outcome
- Expected Return | 9.75% | Typical outcome
- Realistic Downside Return | 4.83% | Realistic bad outcome
- Worse Case Scenario | -3.06% | Very unlucky outcome
Using the Five Number Framework
The Five Numbers Framework is a simple Quantamental tool to understand an investment’s characteristics by building the right expectation in relatively easy (though approximate) terms.
It has a few advantages:
- It only requires the investors to know the time frame of investing.
- Rather than an exact number (which is misleading), it provides a range that helps set the expectation around the possible outcomes.
- It can compare multiple investments over multiple asset classes and over multiple time-frames.
Five Numbers — Across Market Cap
Below is a comparison of NIFTY50, NIFTYNEXT50, and NIFTY MIDCAP150 returns over the Five Numbers Framework (from 1-Apr-2005 to 1-Jul-2020).
The Five Number Framework returns are consistent to indicate which is the better investment. At the same time, investors expectation is set as well without engaging in complex mathematics.
The graph above shows an easy-to-understand picture when considering which investment to select. It sets the expectation of the investor right regarding the range of returns possible from each investment option.
However, immediate historical returns show a different and confusing picture. Where either Index is performing better than the others in different time frames. As shown below:
NIFTY50 |NIFTYNEXT50 | NIFTY MIDCAP150
Historical Returns (Ending 01-Jul-2020)
- CAGR over 5 Years: 4.29% | 5.11% | 5.37%
- CAGR over 3 Years: 3.08% | -0.64% | -1.84%
- CAGR over 1 Year: -12.07% | -6.23% | -11.29%
- CAGR over 6 Months: -26.76% | -17.18% | -21.0%
- CAGR over 3 Months: 155.65% | 141.89% | 167.91%
- CAGR over 1 Month: 106.61% | 89.19% | 168.92%
Some rules
Five rules need to be followed when choosing an investment using the Five Numbers Framework. These are:
- Start with the Expected Return. This is the rate of return to consider when financing a goal or giving a fair picture of how the investment will turn out. If two investments have a similar Expected Return, then choose the one with the higher Realistic Downside Return (if looking for a safety) or higher Realistic Upside return (if looking for performance).
- Do consider the Worse Case Scenario to set an expectation that this too may happen if the investor is extremely unlucky.
- The Realistic Downside Return should at least be positive for an investment to qualify.
- In case of a time-sensitive or critical goal, use the Realistic Downside Return rate to compute how much funding does the goal need. Using this rate of return to fund a goal, there is a high probability that the investors will meet their goal on time.
- In case of an open or aspirational goal, use the Realistic Upside Return rate to compute how much funding does the goal need. Using this rate of return to fund a goal, the funding amount can be lower and the excess funding can be channeled back to more critical goals.
A Five Numbers Application Example
The above rules can be understood with the example described below.
An investor wants Rs. 500,000 in 5 years by investing in NIFTYNEXT50 today. Ordinarily, the investors should assume an Expected Return of 13.04% and start with Rs. 270,900.16 to reach the target value. In case the investment performs well and gives a return similar to the Realistic Upside Return of 18.83%, the investors will reach the goal in 3.55 years. This is an acceptable outcome.
However, if the goal is critical then the investors will need to start with a higher amount of Rs. 336,535.66 expecting the Realistic Downside Return rate of return of 8.24%. In this case, if NIFTYNEXT50 gives the Expected Return of 13.04%, then the investors will reach the goal in 3.22 years. This is an acceptable scenario as well.
The important thing is that the NIFTYNEXT50’s Realistic Downside Return is positive for it to be selected as an option for investment.
Five Numbers across time frames
Common investing wisdom tells us that:
Risk or the possible range of outcomes decreases as time periods of holding increases for the same investment.
The graph below gives us an intuitive understanding that the shorter the time period of investment, the more the variety of outcomes are possible. This implies short term returns are heavily dependent on luck. Another thing to notice is that the realistic downside returns of periods up to 1 year are negative. This means if investment in the NIFTY50 index (or stock markets) for up to 1 year is not a good strategy. It violates rule number 3.
When we plot the graph of the 5 numbers of NIFTY50 returns across time-frames we get an intuitive picture of how risk decreases with time.
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