Math Problem Statement

You are considering how to invest part of your retirement savings.You have decided to put $ 200 comma 000 into three​ stocks: 67 % of the money in GoldFinger ​(currently $ 23​/share), 18 % of the money in Moosehead ​(currently $ 96​/share), and the remainder in Venture Associates​ (currently $ 8​/share). Suppose GoldFinger stock goes up to $ 31​/share, Moosehead stock drops to $ 50​/share, and Venture Associates stock drops to $ 2 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 the problem and calculate the answers step by step.

Given:

  • Total investment: $200,000
  • GoldFinger: 67% of the total investment, currently priced at $23 per share.
  • Moosehead: 18% of the total investment, currently priced at $96 per share.
  • Venture Associates: The remainder of the investment, currently priced at $8 per share.

New stock prices after changes:

  • GoldFinger: $31 per share.
  • Moosehead: $50 per share.
  • Venture Associates: $2 per share.

Step 1: Calculate the amount of money invested in each stock.

  • GoldFinger:
    67%67\% of $200,000 =
    0.67×200,000=134,0000.67 \times 200,000 = 134,000

  • Moosehead:
    18%18\% of $200,000 =
    0.18×200,000=36,0000.18 \times 200,000 = 36,000

  • Venture Associates:
    The remainder, which is 100%67%18%=15%100\% - 67\% - 18\% = 15\%, of $200,000 =
    0.15×200,000=30,0000.15 \times 200,000 = 30,000

Step 2: Calculate how many shares were bought.

  • GoldFinger:
    Number of shares = 134,00023\frac{134,000}{23}

  • Moosehead:
    Number of shares = 36,00096\frac{36,000}{96}

  • Venture Associates:
    Number of shares = 30,0008\frac{30,000}{8}

Step 3: Calculate the new value of each stock after the price change.

  • GoldFinger:
    Value = Number of shares ×31\times 31

  • Moosehead:
    Value = Number of shares ×50\times 50

  • Venture Associates:
    Value = Number of shares ×2\times 2

Step 4: Add the values to find the total new portfolio value.

Step 5: Calculate the return on the portfolio.

The return can be calculated as:
Return=New Portfolio ValueOriginal InvestmentOriginal Investment×100\text{Return} = \frac{\text{New Portfolio Value} - \text{Original Investment}}{\text{Original Investment}} \times 100

Step 6: Calculate the new portfolio weights based on the new value of each stock.

Let me calculate these values.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can guide you through the steps manually or assist with any other question.

Let me know how you'd like to proceed! Meanwhile, here are 5 related questions to consider:

  1. How do stock splits affect a portfolio’s value?
  2. What is the difference between portfolio return and portfolio risk?
  3. How does the weighted average cost of capital (WACC) impact investment decisions?
  4. What are other common methods to rebalance a stock portfolio?
  5. How does diversification help in reducing risk in a stock portfolio?

Tip: Always monitor the market trends, as external factors (like earnings reports) can drastically influence stock prices.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Portfolio Allocation
Percentage Calculations
Stock Valuation

Formulas

Amount Invested = Percentage × Total Investment
Number of Shares = Amount Invested ÷ Share Price
New Portfolio Value = Number of Shares × New Share Price
Return = (New Portfolio Value - Original Investment) ÷ Original Investment × 100
Portfolio Weights = New Value of Each Stock ÷ New Portfolio Value

Theorems

Basic principles of portfolio management and return calculation

Suitable Grade Level

College Level (Finance/Investment)