Planit:Where do Rates of Return Come From? (Malaysia)
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Rates of Return for Asset Classes and Portfolios
PlanPlus Planit is populated with historical indices data for all asset classes used in the Asset Allocation Screen. For Canada, our goal is to use data is to retain data going back to 1950, when identifying the long term historical return for each asset class. Some asset classes use shorter time frames simply because data is not available going back this far. In some other jurisdictions like Malaysia or China, indices data is only available for a much shorter time period and in those cases our returns will be based on the longest period possible. The Investment Policy Statement document for most jurisdictions will include the assumptions used for rates of return which will identify the indices used and the time period covered. This is a valuable source for details about the return assumptions used on your site.
Regardless of the actual time period used, the calculation to identify the rate of return for the Current and Target portfolio is the same. We do a weighted return calculation that is based on the asset allocation of the portfolio. The following illustrates a simple example for a portfolio that has 10% in Cash, 75% in Fixed Income and 15% in Domestic Equities:
In this example, you’ll notice that we use the historical real rate of return for each asset class. This is simply the historical returns from the benchmark indices net of inflation. We then take that “Real Rate of Return” and add back in the client’s inflation assumption from the Personal Information screen to get a forward looking projected return.
This allows us to use history as a benchmark for our rates of return while tempering those returns with inflation rates that are appropriate given conservative long term projections. This in effect means we use hisorical returns but adjust those historical returns through the inflation assumption to make the returns more forward looking.
One other consideration is the fact that advisors can elect to use the “Return Reduction” feature on the Asset Allocation Screen or the Planning Assumptions screen in version 5.6 and higher, to further adjust the projected long term returns downwards. This allows advisors to present projections that they are comfortable with and create what they feel are realistic expectations in the mind of the client. It also allows you to use long term rates of return that are more conservative in your long term planning to help protect the integrity of the long term analysis.
The rates of return you use for your clients are a key element in your planning assumptions. Corporate compliance departments and advisors alike recognize that it’s important for you to be able to support your assumptions with reasoning that is prudent and practical as opposed to merely choosing a rate of return out of thin air! It’s for this reason that the historical returns are the foundation of our return projections, but we also don’t want to tie advisors hands, but rather allow them to modify downwards the assumptions in order to be conservative. This approach allows us to reference historical returns in our documents as the basis for the return projections, which indeed they are.
Standard Deviation
In PlanPlus Planit we identify the "Risk" associated with a portfolio on both the Asset Allocation screen and in documents by using the term "Standard Deviation" The math to identify "Standard Deviation" is very simple when you are looking at a single asset class. It’s merely measures the degree of deviation that takes place over the time period being measured. For further information on the formulas and calculation method to identify Standard Deviation, you can use the following link: [1].
In PlanPlus Planit you also have to consider that our SD calculations are for multiple asset classes. So when you calculate the SD for a portfolio made up of 8 or 10 asset classes, you have to consider the SD for each of these. You might think it’s just a simple weighted average calculation but it’s more complex than that. Let look at some actual numbers to explain.
Let’s say you have two asset classes you are using. One has a historical SD of 3% and the other has a historical SD of 9%. If the portfolio were 50/50, you’d do a simple weighted average calculation like this:
3% x 50% = 1.5% 8% x 50% = 4.0% SD = 5.5%
If these asset classes were positively correlated to each other (had a correlation of 1) the above calculation would be correct. However, assets are only positively correlated to themselves since you virtually never will have two asset classes that behave exactly the same.
Let’s say that these two asset classes were perfectly negatively correlated (had a correlation of –1). In that case the SD would actually be 0%. This is because the risk is totally eliminated because when one goes up, the other goes down which effectively reduces, or in this perfect example, completely eliminates the risk. That’s why the correlation has to be factored into the calculation. You want to recognize how the asset classes behave against each other and recognize how combining asset classes that are negatively correlated will reduce risk. In PlanPlus Planit our measurement of risk recognizes BOTH standard deviation and correlations.
Here’s an example. Take a portfolio that is 50% Cdn Fixed Income and 50% Canadian Equities. Using the Weighted average calculation, the SD might be:
3.49% x 50% = 1.75% 16.37% x 50% = 8.19% SD = 9.94%
But the SD that’s reported in the software is say 9.5%. Thus the risk is reduced from 9.94% to 9.5% due to how these two asset classes are correlated. Not a huge impact, but with a broader cross section of asset classes, you’ll see more impact through the recognition of how the assets are correlated to each other.
The measurement of Risk in PlanPlus Planit is very sophisticated. The measurement of Standard Deviation combined with correlations means that the calculation is complex and even excel spreadsheets are not able to do this easily. Inside the tables of PlanPlus Planit we maintain the history of every asset class going back to 1950 (where available) and the standard deviations are measured using this data combined with the correlations from a correlation matrix table. The Algorithms to do these calculations are not math for the faint of heart!
Sharpe Ratio Calculation Explained
The formula for the calculation of the Sharpe Ratio is as follows:
(Portfolio Return – Cash Return) divided by the Standard Deviation for the portfolio.
Translating this to a number using a portfolio return of 5.7%, a cash return of 1.84% and a Standard Deviation for the portfolio of 7.45 would result in a Sharpe Ratio of:
(5.07 – 1.84) divided by 7.45 = Sharpe Ratio of .43