Detailed Explanation

Given Information:

• Stock purchase price: $100
• Initial margin: 50% (so investor puts up $50, borrows $50)
• End of year stock price: $95
• Deflation: 2% (prices decreased by 2%)
• Non-dividend paying stock

Step 1: Calculate Nominal Return Nominal return = (Ending value - Beginning value) / Beginning value = ($95 - $100) / $100 = -$5 / $100 = -5% or -0.05

Step 2: Calculate Leveraged Return With 50% margin, investor invests $50 of their own money and borrows $50.

Equity at beginning = $50 (investor's own money) Equity at end = Ending stock value - Loan amount = $95 - $50 = $45

Leveraged return = (Ending equity - Beginning equity) / Beginning equity = ($45 - $50) / $50 = -$5 / $50 = -10% or -0.10

Step 3: Calculate Real Return Real return = (1 + Nominal return) / (1 + Inflation rate) - 1 Since there's deflation of 2%, inflation rate = -2% = -0.02

Real return = (1 + (-0.05)) / (1 + (-0.02)) - 1 = (0.95) / (0.98) - 1 = 0.969387755 - 1 = -0.030612245 or approximately -3.06%

Step 4: Compare Returns

• Nominal return: -5%
• Leveraged return: -10%
• Real return: -3.06%

The real return (-3.06%) is the greatest (least negative) among the three.

Why Real Return is Greatest:

1. Deflation effect: With 2% deflation, the purchasing power of money increases. This makes the real return higher than the nominal return.
2. Leverage magnifies losses: When the stock price declines, leverage amplifies the loss on the investor's equity.
3. Mathematical relationship: Real return = (1 + nominal return)/(1 + inflation) - 1. When inflation is negative (deflation), the denominator is less than 1, which increases the real return relative to nominal return.

Key Concept: Real return adjusts nominal return for inflation/deflation. During deflationary periods, real returns are typically higher than nominal returns for the same investment.