3.Suppose that you have $30,000 in a bank account earning an interest rate of 6%per year.At the same time you have an unpaid balance on your credit card of $14,000 on which you are paying an interest rate of 18%per year.What is the arbitrage opportunity you face? Answer:You could take $14,000 out ofyour bank account and pay down your credit card balance. You would give up 6%per year in interest earnings($840 per year),but you would save 18%per year in interest expenses (S2,520 per year).Therefore,the arbitrage opportunity is S1,680 per year. 4.Use the data in the table below to compute both the DIJ-type index and the market-weighted index for a hypothetical two-stock index.Discuss which index more accurately reflects the reality of the market. Stock Price Market Value Company Base year Now Number of Shares Base Year Now Stock 1 $20 $30 100 million $2 billion $3 billion Stock 2 $10 $2 50 million $500 million $100 million Total $2.5 billion $3.1 billion Answer: DJⅡtype index Average of current stock prices x100 Average of stock prices in base year =30+2/2 x100 20+10/2 =106.67,indicating an increase of 6.67% market-weighted index =0.8x30/20)+(0.2x2/10)x100 =1.2+0.049x100 124,indicating an increase of 24% The market-weighted index shows a 24%increase,which reflects what has actually happened to the total market value of all stocks:2.5 billion to 3.I billion is growth of 0.6 billion,which as a percent is 0.6/2.5)=24% 5.You invest in a stock that pays $2 per quarter and costs you $50.50 per share.At the end of the year you expect the stock price to be $59.50.What is the expected rate of return on this stock?What is the realized rate of return if the price of the stock is $52 at the end of the year? Answer: Expected rate ofreturn S2(4)+$59.50-S50.50 S50.50 33.66%per year Realized rate of return =$2(4)+$52-$50.50 s50.50 =18.81%per year 2-192-19 3. Suppose that you have $30,000 in a bank account earning an interest rate of 6% per year. At the same time you have an unpaid balance on your credit card of $14,000 on which you are paying an interest rate of 18% per year. What is the arbitrage opportunity you face? Answer: You could take $14,000 out of your bank account and pay down your credit card balance. You would give up 6% per year in interest earnings ($840 per year), but you would save 18% per year in interest expenses ($2,520 per year). Therefore, the arbitrage opportunity is $1,680 per year. 4. Use the data in the table below to compute both the DIJ-type index and the market-weighted index for a hypothetical two-stock index. Discuss which index more accurately reflects the reality of the market. Stock Price Market Value Company Base year Now Number of Shares Base Year Now Stock 1 $20 $30 100 million $2 billion $3 billion Stock 2 $10 $2 50 million $500 million $100 million Total $2.5 billion $3.1 billion Answer: DJI type index = Average of current stock prices x 100 Average of stock prices in base year = (30 + 2)/2 x 100 (20 + 10)/2 = 106.67, indicating an increase of 6.67% market-weighted index = (0.8 x 30/20) + (0.2 x 2/10) x 100 = (1.2 + 0.04) x 100 = 124, indicating an increase of 24% The market-weighted index shows a 24% increase, which reflects what has actually happened to the total market value of all stocks: 2.5 billion to 3.1 billion is growth of 0.6 billion, which as a percent is (0.6)/(2.5) = 24% 5. You invest in a stock that pays $2 per quarter and costs you $50.50 per share. At the end of the year you expect the stock price to be $59.50. What is the expected rate of return on this stock? What is the realized rate of return if the price of the stock is $52 at the end of the year? Answer: Expected rate of return = $2(4) + $59.50 - $50.50 $50.50 = 33.66% per year Realized rate of return = $2(4) + $52 - $50.50 $50.50 = 18.81% per year