Risk management does not eliminate risk — it transforms risk you cannot bear into risk you can. The core tools are hedging, diversification, and insurance. Value at Risk (VaR) measures how bad things could get.
Types of financial risk
Market risk comes from price movements: equities, interest rates, currencies, commodities. Credit risk is the chance a counterparty defaults. Operational risk covers everything else: system failures, fraud, legal liability. Each type requires different measurement and different tools.
A hedge takes an offsetting position to reduce exposure. A wheat farmer sells futures to lock in today's price. An airline buys fuel futures to lock in costs. A perfect hedge eliminates risk but also eliminates upside. Most hedges are partial: reduce variance without zeroing it out.
Value at Risk answers one question: what is the maximum loss over a given period at a given confidence level? A 1-day 95% VaR of $50,000 means there is a 5% chance of losing more than $50,000 in one day. VaR is easy to communicate but dangerous to trust: it says nothing about how bad losses get beyond the threshold. A detailed treatment of VaR models belongs in Finance II.
Scheme
; Parametric VaR (variance-covariance method); Assumes returns are normally distributed; VaR = portfolio_value ร z_score ร volatility ร sqrt(time)
(define (var-parametric value vol confidence-z days)
(* value confidence-z vol (sqrt days)))
(define portfolio 1000000)
(define annual-vol 0.20)
(define daily-vol (/ annual-vol (sqrt 252)))
; 1-day 95% VaR (z = 1.645)
(display "1-day 95% VaR: $")
(display (round (var-parametric portfolio daily-vol 1.6451))) (newline)
; 1-day 99% VaR (z = 2.326)
(display "1-day 99% VaR: $")
(display (round (var-parametric portfolio daily-vol 2.3261))) (newline)
; 10-day 95% VaR (used by regulators)
(display "10-day 95% VaR: $")
(display (round (var-parametric portfolio daily-vol 1.64510))) (newline)
; VaR limitation: says nothing about tail losses
(display "VaR caveat: 5% of the time, losses EXCEED this number")
Python
importmath# Parametric VaRdef var_parametric(value, vol, z, days):
return value * z * vol * math.sqrt(days)
portfolio = 1_000_000
annual_vol = 0.20
daily_vol = annual_vol / math.sqrt(252)
print(f"1-day 95% VaR: ${var_parametric(portfolio, daily_vol, 1.645, 1):,.0f}")
print(f"1-day 99% VaR: ${var_parametric(portfolio, daily_vol, 2.326, 1):,.0f}")
print(f"10-day 95% VaR: ${var_parametric(portfolio, daily_vol, 1.645, 10):,.0f}")
print("VaR caveat: 5% of the time, losses EXCEED this number")
Insurance and diversification as risk tools
Diversification is free risk reduction: holding uncorrelated assets shrinks portfolio variance without sacrificing expected return. Insurance transfers catastrophic risk to someone who can pool it across many policyholders. Both reduce the impact of any single bad outcome, but through different mechanisms — diversification averages across assets, insurance averages across people.