This is an add on to the past cpl posts. Assumptions are the same except where called out. The past two posts are here:
Again,
- No spending
- Still centered on a CRRA style evaluation at fixed horizons
- Human Longevity not in this post at all
- Assumptions mostly as in first bullet pt. link above
Some variations:
A. Different risky portfolios. The "supplement here in Figure 1 is that I was playing with shifting from a less realistic portfolio to a more realistic one with lower volatility in the higher risk portfolio. The one on the left was illustrative with a higher risk P that had .25 std dev. I knew this would bend the CRRA utility a bit. On the right I dialed back the vol in the higher risk portfolio. Still illustrative tho. Close to real equity portfolio in real terms? idk, no idea. Depends on inflation and stationarity stuff. Inflation = 3% (heh) then 10% with 17% vol is maybe weak sauce for an equity portfolio but maybe left and right are a good bracket. You tell me.
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| Figure 1 Three horizons in each panel |
B. Different Risk Aversions -- same horizon -- Higher risk portfolio. The other game I played is going up the chain in CRRA coefficients. This was not scientific nor was it comprehensive. I played with going to RA = 1 with the right side of Figure 1 at the horizon T = 20 and rendered in Figure 2. where the green line is RA = ~1 and the blue line is RA = 3 when using the higher risk portfolio. The thing missing is RA = 2 but that can be inferred visually if one thinks about it. Again Figure 2 is all at T= 20.
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| Figure 2 |
C. Different Risk aversions - Lower risk portf -- several horizons. Here I am taking three horizons -- 10, 20 and 50y -- and shifting from RA = 3 to RA = 4. This isn't scientific, just looking at what happens incrementally, the movement. Basically one could guess here on RA = 2 and RA = 5 and get thereafter a sense of how the model moves across several RA coefficients. Or I can anyway. This doesn't prove much. Just looking.
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| Figure 3. Three horizons with increasing risk aversion for a "normalish(?)" risk-portfolio |
Conclusions?
- No, not really much, I'm all over the place in this post
- The model is super-sensitive to the risky portfolio assumptions
- The range of "optimal" portfolio allocations is still in a middle ground of 30-80% or more
- Low risk aversion allows very risky portfolios, but...
- One could take a mid-portfolio and lever it along a CML; haven't run that one yet
- The near-horizon appears to forgive wide ranges of AA but this violates my priors. TBD
- Rising risk aversion pulls in risk allocation but: "duh"
- What do you see?
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