Time value of money (TMV) for level 1 CFA Exam

Securities usually have one or more type of risk

  • Default risk – risk of a borrower not make the payments on time
  • Liquidity Risk – cost of selling low liquid assets to transfer to cash (e.g. as with banks and day to day cash flows)
  • Maturity risk – The longer the maturity of a bond the risk as we are trying to determine things that are out of our view e.g. for 10 year bonds.
can be written as:
Required interest rate on a security = Nominal risk free rate + defat risk premium + Liquidity premium + maturity risk premium
A ” rate ” can also be interpreted as the ” discount rate ” and both are interchangeable.
Future value (compound value) of a single sum:
This is the amount a deposit will grow over a specific amount of time with interest being paid to the principal at n intervals.
DV = PV(1+I/Y)n
  • PV = amount of money invested today (the present value
  • I/Y = rate of return per compounding period
  • N = total number of computing periods
Interest rates are our measure of the time value of money, although risk differences in financial securities lead to differences in their equilibrium interest rates . Equilibrium interest rate are the required rate of return for a particular investment.
Interest rate can also be views as the discount rate, it can also be seen as the opportunity cost of the current consumption.
Real risk-free rate of interest is a theoretical rate on a single period loan that has no expectation of inflation in it, it refers to an investor’s increase in purchasing powder (after adjusting for inflation).  since expected inflation in future periods is not zero, the rates we observe on U.S T-Bill are risk-free rates but not real rates of return, they are nominal risk free rates because they contain an inflation premium. the approximate relation here is.

Moninal Risk-free rate = Real risk-free rate + expected inflation rate

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