CFA Level 1 - Quantitative Methods & Fixed Income Analysis

For periodic compounding: $FV=PV(1+r{)}^n$

For continuous compounding: $$\begin{gathered} FV=PV \\ cdot{e}^{r \\ cdott} \end{gathered}$$

where $PV$ is present value, $r$ is the rate per period, $n$ is total periods, and $t$ is time in years.

Measures the actual annual interest earned when compounding occurs more than once per year:

where $r_s$ is the stated annual rate and $m$ is the compounding frequency per year.

• Decision Rule: Accept projects if $NPV>0$. Among mutually exclusive projects, accept the one with the highest positive $NPV$.

The discount rate that forces the present value of future cash flows to equal the initial outlay ($NPV=0$):

• Decision Rule: Accept projects if $IRR>r$ (required rate of return).

Updates the prior probability of an event given new information:

where $P(A)$ is the prior probability, $P(B|A)$ is the likelihood, and $P(A|B)$ is the posterior probability.

• Expected Return: $E(R_p)=w_{A}E(R_A)+w_{B}E(R_B)$
• Variance: $$\begin{gathered} sigm{a}_p^2=w_A^2 \\ sigm{a}_A^2+w_B^2 \\ sigm{a}_B^2+2w_A{w}_B \\ sigm{a}_A \\ sigm{a}_{B}h{o}_{A,B} \end{gathered}$$

where $w$ represents portfolio weights and $h{o}_{A,B}$ is the correlation coefficient.

A normal distribution standardized to mean $mu=0$ and variance $sigm{a}^2=1$.

Represents the number of standard deviations an observation $X$ lies from the population mean $mu$.

States that for any population with mean $mu$ and variance $sigm{a}^2$, the sampling distribution of the sample mean $barX$ approaches a normal distribution with mean $mu$ and variance $$\begin{gathered} frac \\ sigm{a}^{2}n \end{gathered}$$ as sample size $$\begin{gathered} n \\ ge30 \end{gathered}$$.