Week4_FIN2062a_Feb2_PracticeQs_Ch1516_Answers

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Feb 20, 2024

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QUIZ #2 FINANCIAL CALCULATION REVIEW CHAPTER 15: INTRODUCTION TO PORTFOLIO MANAGEMENT Rate of Return (Individual Security) Question #1 : On January 1, 2020, an investor purchases one share of Canadian Pacific Ltd on the TSX for $20.00. On January 1, 2021, the share was sold at a price of $22.00. It’s dividend yield for the most recent period is 3%. What is the rate of return for the investor? Formula: Rate of Return (%) = Cash Flow ($) + (Sale Price – Purchase Price) Purchase Price Rate of Return (%) = $0.60 + ($22.00 - $20.00) $20.00 Rate of Return (%) = $0.60 + $2.00 $20.00 Rate of Return (%) = $2.60 = 13.0% $20.00 Question #2 : On October 12, 2019, an investor purchases a bond with a face value of $100.00 with one year to maturity. It pays an interest rate of 6% annually and the purchase price is $101.50. What is the rate of return for the investor? Formula: Rate of Return (%) = Face Value ($) + Interest ($) - Sale Price Purchase Price Rate of Return (%) = $100.00 + $6 - $101.50 $101.50 Rate of Return (%) = $106.00 - $101.50
$101.50 Rate of Return (%) = $4.50 = 4.43% $101.50 “Real” Rate of Return (Individual Security) Formula: “Real” Rate of Return (%) = “Nominal” Rate of Return - Inflation Rate of Return (Portfolio) Question #3 : Michael and Terry are comparing the rates of return on their stock portfolios to see whose advisor is doing a better job. They have exactly the same rates of return for the equities (10%), fixed income (6%) and cash (3%) in each of their portfolios. But Michael’s portfolio has a 70% equity, 25% fixed income and 5% cash allocation while Terry’s portfolio has a 30% equity, 60% fixed income and 10% cash allocation. Which advisor has generated a better rate of return? Formula: Rate of Return (%) = (r-1 x w-1) + (r-2 x w-2) + …. (r-n x w-n) Michael = (70% x .10) + (25% x .06) + (5% x .03) = (0.07) + (0.015) + (0.0015) = (0.087) = 8.7% Terry = (30% x .10) + (60% x .06) + (10% x .03) = (0.03) + (0.036) + (0.003) = (0.069) = 6.9%
Sharpe Ratio Question #4 : So, we now know that Michael’s portfolio generated the higher rate of return last year. But, we have also learned that we should take into account the level of “risk” that each portfolio is subject to. If Michael’s advisor tells him that the “standard deviation” for his portfolio = 20 and Terry learns that the “standard deviation” for his portfolio = 10, then which advisor has constructed the better portfolio based on a current “risk-free rate of return” of 1.5%? Formula: Sharpe Ratio = Portfolio Return (%) - “Risk Free” Return) Standard Deviation Michael = (0.087) - (0.015) 20 = 0.072 = 0.0036 20 Terry = (0.069) - (0.015) 10 = 0.054 = 0.0054 (Larger is better!!) 10 Portfolio Re-Balancing Question #5 :
Following this discussion, Michael decides to talk with his advisor (who he hasn’t seen in 3 years). Together they decide that Michael’ portfolio needs to be re-balanced. Remember that his base portfolio is 70% equity, 25% fixed income and 5% cash and the annual rates of return for each asset class has been: equities 10%, fixed income 6% and cash (3%). Michael’s original investment 3 years ago was $100,000. What is the process for re-balancing Michael’s portfolio? Step #1: Determine the original dollar value invested in each asset class. Equities = $100,000 X 70% = $ 70,000.00 Fixed Income = $100,000 X 25% = $ 25,000.00 Cash = $100,000 X 5% = $ 5,000.00 Total = $100,000.00 Step #2: Determine the current weighting and dollar value in each asset class. Equities = $70,000 X 10% = $ 77,000.00 Fixed Income = $25,000 X 6% = $ 26,500.00 Cash = $5,000 X 3% = $ 5,150.00 Total = $108,650.00 Step #3: Using the base portfolio allocation, determine what the proper amount of money should be in each asset class for the current portfolio value. Equities = $108,650 X 70% = $ 76,055.00 Fixed Income = $108,650 X 25% = $ 27,162.50 Cash = $108,650 X 5% = $ 5,432.50 Total = $108,650.00 Step #4: Determine necessary adjustments by asset class. Current Target Value Value Action Equities $77,000.00 $76,055.00 Sell $945.00 Fixed Income $26,500.00 $27,162.50 Buy $662.50
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