RATES AND RETURNS

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SEE THIS JUST BEFORE EXAM

  1. The rule is simple: first identify the holding-period return, then ask, “How many of these periods fit into one year?” If it is monthly, compound 12 times. Weekly, 52 times. Quarterly, 4 times. Daily, usually 365 times in this module. If it is 15 days, compound by 365 divided by 15. If it is 18 months, one year is two-thirds of that period, so raise one plus the return to two-thirds, then subtract one.
  2. If CFA says “compare returns across different horizons,” annualize.
  3. If CFA says “continuously compounded,” think natural log.
  4. If CFA gives multiple log returns over time, add them.
  5. If CFA gives ending and beginning price, use log of ending over beginning.
  6. If CFA asks why continuously compounded returns are useful, the clean answer is: because multi-period continuously compounded returns are additive, while ordinary holding-period returns compound multiplicatively.

LEVERAGED RETURN

  1. Imagine you have 70 of your own money, but you want to buy 100 worth of assets. So you borrow 30. Now the asset does not care where the money came from. It earns a return on the full 100. That is the key idea behind leverage.
  2. Suppose the asset earns 8 percent. On 100 of assets, that creates 8 of profit. But the borrowed 30 is not free. If the borrowing cost is 5 percent, you must pay 1.5 to the lender. So the profit left for you is 8 minus 1.5, which is 6.5.
  3. Now slow down, because this is where CFA can trick you. Your return is not 6.5 divided by 100, because you did not invest 100 of your own money. Your own money was only 70. So your leveraged return is 6.5 divided by 70, which is about 9.29 percent.
  4. That is the whole mechanism. Leverage helps when the asset return is higher than the borrowing cost. Here the asset earned 8 percent and debt cost 5 percent, so borrowing added value. But if the asset earned only 3 percent while debt still cost 5 percent, leverage would hurt you, because you borrowed money at a higher cost than the asset earned.
  5. Leverage does not automatically increase return. It increases exposure. If the spread is good, your return rises. If the spread is bad, your return falls faster.
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