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"Relative Risk Aversion" and the Constant Mix Rebalancing Strategy

What is “relative risk aversion” and what do they mean when an investor who has a constant relative risk aversion would utilize a constant mix strategy? (I’m asking why relative risk aversion dictates keeping a constant mix in the portfolio, which may be clarified by the definition of relative risk aversion)

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I guess relative here mean even if you are getting old your risk tolernace still high (relatively) you have a lot of say FC and you are wealthy investor.  in other word, your risk tolerance will not change as your wealther increae or decrease it will be the same, either High or low. The key word for B&H strategy is fixed minimum floor and for CPPM is risk tolerance increases with wealth. but in constant mix. its fixed high or low.   

Glue85 wrote:

I guess relative here mean even if you are getting old your risk tolernace still high (relatively) you have a lot of say FC and you are wealthy investor.  in other word, your risk tolerance will not change as your wealther increae or decrease it will be the same, either High or low. The key word for B&H strategy is fixed minimum floor and for CPPM is risk tolerance increases with wealth. but in constant mix. its fixed high or low.   

I’m thinking your use of the word “fixed” made this click for me - it’s CONSTANT so you just DON’T ADJUST your positions relative to the value of the market, or relative to the value of other assets (at 40% E and 60% B, and keep it). Thanks!

I did a problem in the Schweser QBank that helped me understand the differences between the constant mix and buy-and-hold strategies.

It went something like:

Investor has stock / bond allocation of 70% / 30% and total assets = $100 ($70 in stock, $30 in bonds). Assume the stock market goes up 10%, what will the new allocations be for:

  • Buy-and-hold strategy: Increase in stock market by 10% results in stocks now worth $70 * 1.10 = $77 and bonds remain unchanged at $30, all else equal. Computing the new allocations, we get a stock / bond allocation of 72% / 28%. The investor’s portfolio is effectively more exposed to equity markets given the increase in the stock market.
  • Constant mix strategy: Increase in the stock market by 10% results in stocks worth $77, same as above, and bonds remain unchanged at $30, all else equal. However, under a constant mix strategy, we want to keep a constant mix at 70% / 30%, not 72% / 28% as with the buy-and-hold strategy. So we rebalance out portfolio that is now worth $107 to get back to 70% / 30%. The rebalance tells us we need 70% * $107 = $74.90 in stocks and 30% * $107 = $32.10 in bonds, getting us back to our original constant mix.

Hope this helps!

OMGMileyCyrus

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JSobes wrote:

What is “relative risk aversion” and what do they mean when an investor who has a constant relative risk aversion would utilize a constant mix strategy? (I’m asking why relative risk aversion dictates keeping a constant mix in the portfolio, which may be clarified by the definition of relative risk aversion)

In a constant mix strategy, your % of stocks and bond holdings are rebalanced to acheive a constant mix of say 70/30 (just as in the example given above). Essentially you would like maintain the same amount of risk (mix) in your portfolio, regardless if the value moves up..or down. 

The statement is saying that the investor maintain a constant risk aversion, therefore a CM strategy is the obvious choice.

If you draw the diagram it will help you.

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