Morningstar - Q4 2020 - 66

Strategies

EXHIBIT 3

Optimal Asset Allocation and Location for Financial Wealth in Isolation
Effective
Tax Rate (%)

Asset Class

Taxable Account

U.S. Large-Cap Stocks

22.79

3.95

U.S. Mid-Cap Stocks

24.50

0.11

U.S. Small-Cap Stocks

25.93 3.66

Global DM Ex-U.S. Stocks

19.34

Emerging-Markets Stocks

20.50

Global REITs

26.39

U.S. Bonds

40.00

Municipal Bonds

EXHIB IT 3 shows the optimal portfolio for the
joint problem with the allocations in the
two accounts broken out. Note that the three asset
classes with the lowest effective tax rates are
allocated to the taxable account. U.S. largecap stocks, having the third-lowest effective tax
rate, are only partially located in the taxable
account because there was not enough room after
locating the global developed markets
excluding U.S. stocks and emerging-markets
stocks in the taxable account.

Tax-Advantaged Account

8.38

31.97
14.08
2.14
14.49

0.00

Global Bonds Ex-U.S.

40.00

Cash

40.00

21.23

0%

Source: Morningstar.

10

20

30

40

1
U ( E,V ) = u (1 + E ) + u"(1 + E )V
The Joint Allocation Problem
in a Net Worth
2
Framework
O -1
(1 + E ) O , O ≠ 1
- 1 of Quant U ("A Better
) =2020 issue
uIn(1the
+ EQ2
Retirement Spending
) , for Everyone"),
ln(1 + ERule
O =1
I discussed the concept of net worth ( W ), which
-1
is (financial
human capital
u"
1 + E ) = wealth ( F ) plus
1+ O
(1 + value
E ) O of future liabilities ( L):
( H ) less the present
m

∑

m

m

∑∑

xi xj
W = F + HU- L xi i ,
i =1
i =1 j=1
max
x , x , ... , x
1

EXHIBIT 4

Expected Return
12%

INDIFFERE

NCE C

URVE

m

ij

m

Human capital is the present value of
s.t. xi = 1, xi ≥ 0
future incomei =1from
all sources, including wages
and social insurance. Liabilities consist
max U ( x ' , x ' x ) s.t. x ' = 1, x ≥ 0
of nondiscretionary spending, such as for food,
clothing, and shelter. Net worth is the value
of the
= ( 1investor's
-  i ) i resources available for
Ai
discretionary spending, such as the incremental
= ( 1 -  i ) i
Ai
cost
of dining out and traveling for leisure.
The net worth approach to financial planning is
sometimes
)' balance
) ' (approach.
max U ( Tcalled
+ Bthe
, ( T A + sheet
T A+ B)
A
B
,
A B
s.t. A' = , B' = 1 - , A ≥ 0, B ≥ 0
We can model
both H and L like assets. Their
changes in value over time are their returns. The
return on net worth ( R˜W ) is:

∑

Risk and Expected Return of Net Worth

OR
TW
T NE
N
I
O
J

2

i j

FFI
TH E

O
T FR
CIEN

NTIE

R

9

6

Optimal Joint Net Worth Portfolio

3

(

)

0
0%
Standard Deviation

10

20

30

R˜W = F R˜F + H R˜H - L R˜L
W
W
W

Source: Morningstar.

To illustrate how the joint MVO problem works,
I estimated the effective tax rates for the
asset classes in the previous issue of Quant U
using 40% as the tax rate on ordinary income
and 20% as the long-term capital gains rate.
Assuming that the investor's assets are split 50/50
between the taxable and tax-advantaged
accounts, I traced the efficient frontier in aftertax

66

Morningstar Q4 2020

expected return and standard deviation on
the portfolio as a whole ( EXHIB IT 2 ). I then found
the optimal portfolio using 22.7% as the level
of risk tolerance, the value that I used for the MVO
problem without taxes. To show how the optimal
joint portfolio is determined, I included the
tangent indifference curve for the joint problem
in E X H I BI T 2 .

where R˜F , R˜H , and R˜L are the returns on financial
wealth, human capital, and the value of
max U EW ( T A + B ) , VW ( T A + B )
liabilities,
respectively. Of these three, the investor
,
A B
only makes
= 1 - , for
≥financial
0, B ≥ 0
s.t. A'allocation
= , B' choices
A
wealth. We model human capital and the value
of liabilities as risky assets or combinations
of asset classes. Because the cash flows of human
capital and liabilities are largely known in advance,
human capital and the value
of liability are
1- 1
O -1
c
both
very
much
like
combinations
, O ≠of1 bonds.
u(c) = { ln(c), O = 1
1- O1

(

1
1+

c~t+1
ct

)

-1
O

~t
= Qt+1



Morningstar - Q4 2020

Table of Contents for the Digital Edition of Morningstar - Q4 2020

Contents
Morningstar - Q4 2020 - CT1
Morningstar - Q4 2020 - CT2
Morningstar - Q4 2020 - Cover1
Morningstar - Q4 2020 - Cover2
Morningstar - Q4 2020 - 1
Morningstar - Q4 2020 - 2
Morningstar - Q4 2020 - Contents
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