Finance & Risk 1&2 Flashcards
What is finance in one sentence?
Finance is the trade in risks across time, i.e. exchanging future contingent cash-flows today to reallocate resources optimally.
How do you compute the present value PV of a future payment π due in k periods at interest rate r?
PV = π × D_k, where D_k = 1/(1+r)^k. PV: present value; π: payment at time k; r: per-period rate; k: periods; D_k: discount factor.
In a one-period arbitrage between two banks, why must the borrowing rate r equal the lending rate R?
If R > r, one can borrow p at r and lend at R to earn (R−r)·p risk-free. No-arbitrage ⇒ R = r.
Define a contingent cash-flow c(t,ω). What makes it an asset or a liability?
c(t,ω) is a payment at time t if state ω occurs. Asset if c(t,ω) ≥ 0 ∀t,ω; Liability if c(t,ω) ≤ 0 ∀t,ω.
State the Law of One Price.
Identical cash-flows with the same risk must have identical prices; otherwise arbitrage profits would exist.
How is variance Var(X) of a random variable X defined? List symbols.
Var(X) = E[(X − E[X])^2], where E[X] is the expected value of X and Var(X) is its average squared deviation from the mean.
What is Value-at-Risk (VaR) at confidence level α?
VaR_α is the smallest loss L such that P(X ≤ −L) ≤ 1 − α, i.e. the worst loss not exceeded with probability α.
How does Expected Shortfall (ES) differ from VaR?
ES_α is the average loss in the worst (1 − α)% of scenarios. It is a coherent risk measure (unlike VaR).
Why does money evolve from barter?
To solve the double-coincidence problem: money is a widely accepted, durable medium that everyone will accept, simplifying multi-party trades.
Describe an arbitrage opportunity in a one-period model.
Borrow amount p at rate r, lend at higher R, and lock in profit (R−r)·p risk-free. Competitive markets remove such opportunities.
