Asset Pricing：Introduction

Asset Pricing：Introduction

Asset pricing is the study of the value of claims to uncertain future payments.

Two components are key to value an asset: the timing and the risk of its payments.

是什么决定了financial claims的价格？为什么价格会随时间变化，为什么不同资产的价格会不同：

1. Statistical approaches look at statistical relationships between asset prices
2. “Weak” economic approaches look at some basic relations that must hold between asset prices, such as the absence of risk-free profifitable strategies
3. Economic models derive prices from the fundamental characteristics of an economy

假设在时间点 $t$?，我们定义payments { x t + τ } , τ ≥ 1 \{x_{t+\tau}\},\tau\geq1 { xt+τ?},τ≥1??，这些payments的价格为 $p_t\approx {\mathbb{E}}_t{\sum }_{\tau \ge 1}[x_{t+\tau }]$。

另一种考虑financial claims的方式是根据回报：$R_{t+1}=\frac{p_{t+1}+x_{t+1}}{p_{t+1}}?1$?

excess return（超额回报）：two assets $i,j$ 回报之间的difference：$R_{t+1}^e=R_{i,t+1}?R_{j,t+1}$

We can interpret these three representations as follows: we can invest $p_t$ today and get { x t + τ } \{x_{t+\tau}\} { xt+τ?} in the future, or invest 1 unit today and get $R_{t+1}$ in the future, or yet invest 0 units today and get $R_{t+1}^e$?? in the future.

Discount News: $p=E_t[m_{t+1}{x}_{t+1}]$