Syllabus

Chapter 1 – Time Value of Money (TVM)

1. Equilibrium Interest Rates – required rate of return
2. Interest rates = opportunity cost = required rate of return = cost of capital
3. Nominal risk-free rate = real risk-free rate + expected inflation rate
4. Securities’ types of risk:

1. Default risk
2. Liquidity risk
3. Maturity risk (Longer maturity bonds have more maturity risk)

1. Required interest rate on a security = nominal risk-free rate

                                                                 + default risk premium

                                                                 + liquidity premium

                                                                 + maturity risk premium

1. Perpetuity – fixed amount over infinite period of time (把PMT看做dividends)

1. PV = PMT / I (表示投资人愿意成交的股价)
2. I = PMT / PV (表示该股票的投资回报率)

Chapter 2 – Probabilities

1. 满足probability function的两个条件:

1. 0 <= P(X) <= 1
2. ∑p(x) = 1 (sum of probabilities for all possible outcome)

1. Discrete & Continuous Distribution:

1. Discrete

1. P(x) = 0 表示事件x不可能发生
2. P(x) > 0 表示事件x可以发生

1. Continuous

1. P(x) = 0, 即使事件x可以发生
2. P( X1 ≤ X ≤ X2 ) = P (X1 < X < X2) 只有区间的表达方式才有意义

1. Distribution Functions

1. Probability Density Function (pdf) – f(x) 表示区间
2. Cumulative Distribution Function (cdf) – F(x) = P(X≤x) 小于等于该数值
3. Inverse Cumulative Distribution Function – F-1(p) = x = #√p

1. Discrete uniform random variable – 所有可能结果出现的概率相同

1. P(X) - 在discrete中每一个x事件出现的概率都相同
2. F(Xn) = np(X) – n表示X所排列的顺序为第n个
3. P(x)k – probability for a range of outcomes, k = # of possible outcomes

1. Conditional Probabilities

1. Unconditional Probability – 无论如何都会发生的概率，无关其他事件
2. Conditional Probability – 如果B发生，则A一定发生的概率

1. P (A|B) – probability of A, given the occurrence of B
2. P (recession | increase in interest rate) – probability of recession, given…

1. Joint Probability – 2 events both occur – 概率相乘法则

1. P (AB) = P (A|B) x P(B) – “A will occur given B occurs” x “unconditional B occurs”
2. P (A|B) = P (AB) / P(B)

1. Independent and Mutually Exclusive Events

1. Independent – if and only if 以下条件成立:

1. P (A|B) = P (A)
2. P (B|A) = P (B)

1. At least 1 of 2 events will occur:

1. Addition rule for probabilities

1. P (A or B) = P(A) + P(B) – P(AB)
2. P (A or B) = P(A) + P(B) (mutually exclusive)
3. A ∪ B = A or B
4. Mutually exclusive events – P(AB) = 0

1. Multiplication rule for probabilities

1. P (A and B) = P(A) x P(B)
2. A ∩ B = A and B

1. Probability Matrix

1. Unconditional Probabilities: sum of each column and each row