This is one of those things that’s probably simple but my brain never got it.
Reading 6 pg. 34 “assume a portfolio associated with a goal has an expected return of 7% with 10% expected volatility and goal is to be met over next 5 years with 90% confidence. Over the next 5 years this portfolio is expected to produce returns of 35% with a volatility of 22.4%”
The Math → …7% * 5 = 35%…10% * sqr.root(5) = 22.4%
I can’t figure out why returns are sometimes computed arithmetically, and other times computed geometrically i.e. (1.07)^5 - 1? It seems very arbitrary to me.
Is there a rules-based path i can follow to determine which method suits which scenario?
When the return is stated as nominal, you use this:
7% * 5
If the return is stated as effective or compounded, you should use the one you say:
(1.07)^5 - 1
The former is about “simple interest” type of return, so you can assume a yearly waterfall is done (interest or return is distributed). This should be a common scenario in wealth management, most investors require an income from their portfolios. Therefore, the return should be stated in nominal terms, not effective. There is no compound effect because interest is not reinvested.
The latter would be used in a scenario of reinvestment, so no distribution or waterfall is done along the investment horizon. I think the question should provide enough info to differentiate both cases, otherwise I would personally choose the nominal case.
Thanks very helpful. The question doesnt specify but is in the context of “goals-based” portfolios which I guess the default assumption is that these are balance reducing (to your point)