Question

Consider these two scenarios: • Say Johnson & Johnson has an expected return of 6% with a standard deviation of 5% • Puma Biotech, with an unproven cancer drug, has an expected return of 10% with a standard deviation of 15% Which stock is riskier? Puma is riskier Assume each stock trades at $100 per share. For each stock, what range of stock prices captures 95.4% of expected returns? What is the most likely return for each stock?

Answer 1

Expected return :

Johnson & Johnson- 6%

Puma Biotech- 10%

Standard deviation :

Johnson & Johnson- 5%

Puma Biotech- 15%

Stocks with a higher volatility typically have a higher standard deviation. Hence Puma is riskier

The standard deviation is the square root of the variance.

In the case of Johnson & Johnson, Variance is 0.0025,  expected returns = 95.4%

Upper bound number-0.0025+0.954= 0.9565 or 95.65%

Lower bound range- 0.954-0.0025 = 0.9515 or 95.15%

Therefore returns for Johnson & Johnson are likely to fluctuate between 95.15 and 95.65

Similarly,

In the case of Puma Biotech, Variance is 0.0225,  expected returns = 95.4%

Upper bound number-0.0225+0.954= 0.9765 or 97.65%

Lower bound range- 0.954-0.0225 = 0.9315 or 93.15%

Therefore returns for Puma Biotech are likely to fluctuate between 93.15 and 97.65