Question

Assume your portfolio’s initial asset allocation was 40% to bonds and 60% to stocks. You invested 100,000$. After 3 years, stocks went up by 50% and the bonds by 20%.
a. Calculate your portfolio’s asset allocation after 3 years.
b. Calculate and explain how to rebalance your portfolio.

Answer 1

Initial Investment Amount: $ 100,000

Particulars	Stocks	Bonds
Allocation	60%	40%
Absolute Returns in 3 years	50%	20%

Initial investment in stocks = Allocation to Stocks * Investment Amount

Initial investment in stocks = 60% * 100,000

Initial investment in stocks = $ 60,000

Initial investment in bonds = Allocation to bonds * Investment Amount

Initial investment in bonds = 40% * 100,000

Initial investment in bonds = $ 40,000

Post 3 Years

Value of Stocks = Investment in Stocks * (1 + Absolute Return of stocks in 3 years)

Value of Stocks = $ 60,000 * (1 + 50%)

Value of Stocks = $ 90,000

Value of Bonds = Investment in Bonds * (1 + Absolute Return of bonds in 3 years)

Value of Bonds = $ 40,000 * (1 + 20%)

Value of Bonds = $ 48,000

Value post 3 Years	Investment Value	Portfolio Allocation
Stocks	$ 90,000	= 90000 / 138000 = 65.2%
Bonds	$ 48,000	= 48000 / 138000 = 34.8%
Total Value	$ 138,000	100%

Hence, the portfolio’s asset allocation at the end of Year 3 will be 65.2% to Stocks and 34.8% to Bonds. …Answer to Part a

Part b: Rebalancing the Portfolio

There are two ways to rebalance this portfolio:

1. Buy more Bonds from market
2. Sell part of Stocks portfolio

The type of rebalance to be undertaken depends on whether you want to invest more amount or rebalance the existing portfolio without additional investment.

1. Buy more Bonds from the Market

In case you are willing to invest more amount in the market to rebalance the portfolio, more Bonds can be bought in order to bring the portfolio allocation back to 60:40 ratio of stocks and bonds. The same is explained below:

Assuming $ X is invested in bonds. Then,

Value of Stocks: $ 90,000

Value of Bonds: $ 48,000 + $ X

With this investment of $ X in Bonds, the Bonds should make up 40% of the overall investment. Hence,

Allocation to Bonds = Value of Bonds / Total Investment = 40%

Allocation to Bonds = ($ 48,000 + $X) / ($ 90,000 + $ 48,000 + $ X) = 40%

($ 48,000 + $X) = 0.4 * ($ 90,000 + $ 48,000 + $ X)

$ 48,000 + $ X = $ 36,000 + $ 19,200 + $ 0.4 * X

0.6 X = $ 7,200

X = $ 12,000

Hence, with an additional Investment of $ 12,000 in Bonds, the Portfolio can be rebalance to its initial allocation. …. Answer

2. Sell part of Stock Portfolio

In case you don’t want to invest additional amount, part of stocks can be sold in order to bring the portfolio allocation back to 60:40 ratio of stocks and bonds. The same is explained below:

Assuming $ Y is sold from Stocks. Then,

Value of Stocks: $ 90,000 - $ Y

Value of Bonds: $ 48,000

With this sale of $ Y in stocks, the stocks should make up 60% of the overall investment. Hence,

Allocation to Stocks = Value of Stocks / Total Investment = 60%

($ 90,000 – Y) / ($ 90,000 – Y + $ 48,000) = 60%

$ 90,000 – Y = $ 54,000 – 0.6 * Y + $ 28,800

0.4 Y = $ 7,200

Y = $ 18,000

Hence, with a sale of $ 18,000 in Stocks, the Portfolio can be rebalance to its initial allocation. …. Answer