Calculating Bond Purchases to Reach a Portfolio Allocation Target

Summary

The document explains why reaching a target portfolio percentage requires recalculating both the bond holdings and the total portfolio value after new money is invested. The example starts with a £40,000 portfolio holding 40% in bonds and asks how much additional bond investment would raise the bond share to 52%. The proposed but incorrect calculation finds the difference between the current bond value and 52% of the original portfolio.

The accepted answer defines the added investment as an unknown amount and sets the resulting bond value over the resulting portfolio value equal to the target allocation. Solving that relationship gives the stated purchase amount of £10,000. The key lesson is that buying bonds increases the numerator and denominator together. The example is a basic allocation calculation; it does not address price changes, fees, withdrawals, or other portfolio assets beyond the stated setup.

Key ideas

• Adding bonds increases both bond holdings and total portfolio value.
• The target allocation must be applied to the portfolio value after the purchase.
• Set the new bond value divided by the new total value equal to the desired percentage.
• For the stated example, the required bond purchase is £10,000.

Tags

# Reshuffling the weighting of assets in an investment portfolio


# Reshuffling the weighting of assets in an investment portfolio












An investor has a £40,000 portfolio, 40% of which is invested in bonds.The investor wishes to add funds to the portfolio by purchasing bonds so that 52% of the entire portfolio is invested in bonds. What value of bonds should the investor purchase?

My solution is as follows:

40% of the portfolio is £16,000, and 52% of the portfolio is £20,800. Thus in order for the portfolio to be consist of 52% bonds, the investor must purchase £20,800 - £16,000 = £4,800 worth of bonds. Once the investor has spent an extra £4,800 on bonds, this brings the total amount spent on bonds to £20,800, which is 52% of the portfolio.

The actual answer is £10,000. How is my solution wrong and where am I misunderstanding?

## Answer by Alex C (score 1, accepted)

https://quant.stackexchange.com/a/22815

The portfolio is worth 40000, after adding to it it will be worth 40000+X. The portfolio now has 16000 in bonds, after adding it will have 16000+X in bonds. Find X such that (16000+X)/(40000+X) = 0.52

The answer is 10000.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.