To re-balance his portfolio to 70% stocks and 30% bonds, Harvey should move $2,316 from stocks into bonds
Step-by-step explanation:
Harvey invested $50,000 to create a portfolio containing 70% stocks and 30% bonds.
Over the course of a year,
- The value of his stocks increased to 74% and the value of his bonds decreased to 26%.
- The value of his investment, after a year, is $57,900
We need to find What amount should Harvey move from stocks and reinvest in bonds to re-balance his portfolio
∵ The value of his investment, after a year, is $57,900
∵ The value of his stocks increased to 74%
∵ The value of his bonds decreased to 26%
Use the ratio method to find the amount of money in the stock and the amount of money in the bond
→ Stock : Bond : Total
→ 74% : 26% : 100%
→ x : y : 57,900
By using cross multiplication
∴ x × 100 = 74 × 57,900
∴ 100 x = 4284600
- Divide both side by 100
∴ x = 42,846
∴ The amount of money in the stock is $42,846
∵ y × 100 = 26 × 57,900
∴ 100 y = 1505400
- Divide both side by 100
∴ y = 15,054
∴ The amount of money in the bonds is $15,054
∵ The portfolio containing 70% stocks and 30% bonds
Use the ratio method to find the value of 70% and 30% of his investment
→ Stock : Bond : Total
→ 70% : 30% : 100%
→ x : y : 57,900
∴ x × 100 = 70 × 57,900
∴ 100 x = 4053000
- Divide both side by 100
∴ x = 40,530
∴ The amount of money in the stock must be $40,530
∵ y × 100 = 30 × 57,900
∴ 100 y = 1737000
- Divide both side by 100
∴ y = 17,370
∴ The amount of money in the bonds must be $17,370
Now find the difference between the two amount of stocks
∵ 42,846 - 40,530 = 2,316
Add this amount the amount of the bonds at 26%
∵ 15,054 + 2,316 = 17,370
The same amount of bonds at 30%
∴ Harvey must move $2,316 from stocks to bonds
To re-balance his portfolio to 70% stocks and 30% bonds, Harvey should move $2,316 from stocks into bonds
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