I think (hope) I finally see why Essential Spending implies DRRA. Here is an example:
Let’s say I have an investment portfolio of $1,000,000. The Merton share as of 8/4/2024 is 33.4%, so the Planner says to put that much of the $1,000,000 in equities. Trying out the new dateless link feature to see this (I’ve made all the knobs 1 and 0%):
https://tpawplanner.com/link?params=INo ... GAOS6inkEu
Now, let’s increase the portfolio to $2,000,000. The Planner still says to invest 33.4% in equities. The risk is constant even though wealth doubles, so CRRA.
Now, let’s add an Essential Expense of $1000/month to our base case of a $1,000,000 investment portfolio. This has a present value of $308,387. The Planer uses the same Merton share of 33.4%, BUT applies it to ($1,000,000 - $308,387) = $691,613. 33.4% of this is $230,999. And, $230,999 / $1,000,000 = 23.1%, which matches the Planner advice. Essentially, the Planner is saying “If you target some of your investment portfolio for an Essential Expense, remove it from consideration when calculating recommended investment portfolio risk”.
Now, let’s increase the portfolio to $2,000,000. The 33.4% applies to ($2,000,000 - $308,387) = $564,999. And, $564,999 / $2,000,000 = 28.2%, which again matches the Planner advice. So in this case, when I doubled wealth, the risk the Planner produces for the investment portfolio goes from 23.1% to 28.2%. I’m more risk tolerant with the increase in wealth, which means I’m decreasingly risk adverse, so DRRA.
Let’s say I have an investment portfolio of $1,000,000. The Merton share as of 8/4/2024 is 33.4%, so the Planner says to put that much of the $1,000,000 in equities. Trying out the new dateless link feature to see this (I’ve made all the knobs 1 and 0%):
https://tpawplanner.com/link?params=INo ... GAOS6inkEu
Now, let’s increase the portfolio to $2,000,000. The Planner still says to invest 33.4% in equities. The risk is constant even though wealth doubles, so CRRA.
Now, let’s add an Essential Expense of $1000/month to our base case of a $1,000,000 investment portfolio. This has a present value of $308,387. The Planer uses the same Merton share of 33.4%, BUT applies it to ($1,000,000 - $308,387) = $691,613. 33.4% of this is $230,999. And, $230,999 / $1,000,000 = 23.1%, which matches the Planner advice. Essentially, the Planner is saying “If you target some of your investment portfolio for an Essential Expense, remove it from consideration when calculating recommended investment portfolio risk”.
Now, let’s increase the portfolio to $2,000,000. The 33.4% applies to ($2,000,000 - $308,387) = $564,999. And, $564,999 / $2,000,000 = 28.2%, which again matches the Planner advice. So in this case, when I doubled wealth, the risk the Planner produces for the investment portfolio goes from 23.1% to 28.2%. I’m more risk tolerant with the increase in wealth, which means I’m decreasingly risk adverse, so DRRA.
Statistics: Posted by ConstantChrysalis — Mon Aug 05, 2024 11:59 am