What is price of an asset? What is return of an asset and how is asset return calculated? What is multi-period return and how is it related to returns of sub periods?
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Quizzes and Answers
Quiz 1: In the Pokémon card example above, instead of asking your friend Jake to pay 1 dollar 50 cents for the card, if you ask him to pay 2 dollar and 5 cents, how much return would you make from the transaction?
You receive 2 dollar 5 cents from Jake, since you originally paid 1 dollar for the card you make a profit of 1 dollar 5 cents because 2 dollar 5 cents minus 1 dollar is 1 dollar 5 cents. Now take the profit and divide it by 1 dollar (the original price you paid), then you get decimal number 1.05, which is 105% in percentage.
Quiz 2: If your dad bought a stock for a price of 10 dollars one year ago, and sold the same stock for 9 dollars today, how much investment return did he make from the sale?
Your dad bought the stock for a price of 10 dollars, but sold it at a lower price at 9 dollars, so he made a loss from the sale, and the loss is 1 dollar (because 9 dollars is 1 dollar less than 10 dollars). Use the 1 dollar loss and divide it by the purchase price of 10 dollars then you get decimal number 0.1, which is 10% in percentage. Your dad made a 10% loss in return!. This shows you can asset return can be positive or negative. It is OK if you haven’t learned about negative numbers, and simply remember that negative return means a loss is generated from investing in assets.
Quiz 3: Suppose you are investing in a stock called ABC. On day one its price is $10, on day two its price is $8, and on day three its price is $10. What is the asset return between day one and day two? What is the asset return between day two and day three? How about the asset return between day one and day three?
The price of ABC changes from $10 on day one to $8 on day two, a decrease of $2, hence a loss of $2 is generated on day two, and the return is -$2 divided by the reference price of $10, which is -$2 / $10 = -0.2, or -20%.
Between day two and day three, the price increased by $2 from $8 to $10, hence a profit of $2 is made on day three. The return is the profit of $2 divided by the reference price of $8, which is $2 / $8 = 0.25, or 25%.
Between day one and day three, the price stayed the same as $10, hence the total return between day one and day three is 0%.
Quiz 4: Suppose you purchased a stock XYZ on day one for $10. Then on day two the stock price of XYZ went down by 20% compared to day one. On day three its price went up by 20% compared to day two. How much money is your investment worth on day three?
We can solve this by going through each day. On day one the stock price is $10. On day two the price decreased by 20% (which is equal to 0.2) compared to day one, hence the decrease is $10 x 0.2 = $2 in dollar values. This means the price on day two is $2 less than the price of day one, so the price on day two is $10 – $2 = $8.
On day three, the prices went up by 20% (which is 0.2) compared to day two, hence the increase of price is price of day two multiplied by 0.2, which is $8 x 0.2 = $1.6. This means the price on day three is $1.6 more than the price of day two, so on day three the price becomes $8 + $1.6 = $9.6.
From this example you can see that even though the price of stock XYZ first went down 20% and then went up 20%, its price actually differs from the beginning price. Again this can be explained by the multi-period returns.