Math Problem Statement

You are considering how to invest part of your retirement savings. You have decided to put $200,000 into three stocks: 64% of the money in GoldFinger (currently $22/share), 18% of the money in Moosehead (currently $91/share), and the remainder in Venture Associates (currently $9/share). Suppose GoldFinger stock goes up to $37/share, Moosehead stock drops to $68/share, and Venture Associates stock rises to $11 per share. a. What is the new value of the portfolio? b. What return did the portfolio earn? c. If you don't buy or sell any shares after the price change, what are your new portfolio weights?

Solution

Let's break down each part of the problem:

Part (a): New Value of the Portfolio

  1. Initial Allocation in Each Stock:

    • GoldFinger: 64% of $200,000 = 0.64×200,000=128,0000.64 \times 200,000 = 128,000
    • Moosehead: 18% of $200,000 = 0.18×200,000=36,0000.18 \times 200,000 = 36,000
    • Venture Associates: Remaining 18% of $200,000 = 0.18×200,000=36,0000.18 \times 200,000 = 36,000
  2. Initial Shares Purchased:

    • GoldFinger Shares: 128,000225818.18\frac{128,000}{22} \approx 5818.18 shares
    • Moosehead Shares: 36,00091395.60\frac{36,000}{91} \approx 395.60 shares
    • Venture Associates Shares: 36,0009=4000\frac{36,000}{9} = 4000 shares
  3. New Value Calculation with Updated Prices:

    • GoldFinger Value: 5818.18×37215,272.665818.18 \times 37 \approx 215,272.66
    • Moosehead Value: 395.60×6826,900.80395.60 \times 68 \approx 26,900.80
    • Venture Associates Value: 4000×11=44,0004000 \times 11 = 44,000
  4. Total New Portfolio Value: 215,272.66+26,900.80+44,000=286,173.46215,272.66 + 26,900.80 + 44,000 = 286,173.46

Part (b): Portfolio Return

  1. Portfolio Return Calculation: Return=New Portfolio ValueInitial Portfolio ValueInitial Portfolio Value\text{Return} = \frac{\text{New Portfolio Value} - \text{Initial Portfolio Value}}{\text{Initial Portfolio Value}} =286,173.46200,000200,000=86,173.46200,0000.4309 or 43.09%= \frac{286,173.46 - 200,000}{200,000} = \frac{86,173.46}{200,000} \approx 0.4309 \text{ or } 43.09\%

Part (c): New Portfolio We

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Math Problem Analysis

Mathematical Concepts

Investment Calculation
Percentage Allocation
Return on Investment
Weighted Averages

Formulas

Total Value = Shares * New Price
Return = (New Portfolio Value - Initial Portfolio Value) / Initial Portfolio Value
New Weight = (Value of Stock in Portfolio) / (Total Portfolio Value)

Theorems

Basic Percentage and Proportion Theorem

Suitable Grade Level

College/University Finance