Module 1 / Lesson 2.5

Prevention: Self-Protection vs Self-Insurance

4 min read

Lesson guide:

Learning: Read and understand the content material below.
Reflection: As you learn the material below, consider examples from your own experience where you have relied on self-protection (avoiding or reducing risks) versus self-insurance (preparing for losses without outside help).

Key Concepts:

Prevention: Upfront action (in time, money, or effort) to reduce risk before losses happen. Self-protection and self-insurance are the two types of prevention.
Self-Protection: Lower the probability of something bad happening ("e.g. bike locks lower the probability that your bike is stolen").
Self-Insurance: Limit the severity if something bad happens (e.g. fire sprinkler systems reduce damage to your building in the event of a fire).

Making the Investment Up Front

Prevention means you invest in safety now (money, time, hassle), but the benefit comes later, reducing either the frequency (probability) or the severity (size) of bad outcomes.

Self protection is the name for investments that reduce the frequency of a loss
Self-insurance is the name for investments that reduce the severity of a loss.
Some safety investments do both: for example, a anti-lock brakes in cars reduces how often you get in an accident (lower p, self-protection), and lowers the speed at which many accidents happen so that the severity is lower if you get in an accident (lower L, self-insurance).

Examples

Bike theft: Buy a U-lock (self-protection: reduces theft probability)
House fire: Add a sprinkler system (self-insurance: limits damage if fire breaks out)
Data loss: Use strong passwords & MFA (self-protection: reduces breach probability); regular backups (self-insurance: limits loss if incident occurs)

What does self-protection do?

Self-Protection: Spend an amount S to reduce the frequency of the loss (the probability of loss, p):

Without safety investment, probability of loss is p₀.
With safety investment, probability of loss is p₁.
Safety reduces the probability of the loss. The change or improvement in the probability of loss is Δp = p₁ - p₀. (Δp is a negative number since investing in safety lowers the probability of a loss, so that p₁ <p₀.)
Self-protection involves spending S to change the probability of a loss of size L by Δp (lowered from p₀ to p₁).

What does self-insurance do?

Self-Insurance: Spend an amount S to reduce the severity of the loss (the size of loss, L):

Without safety investment, the size of the loss is L₀.
With safety investment, the size of the loss is L₁.
Safety reduces the size of the loss. The change or reduction in the size of the loss is ΔL = L₁ - L₀ (ΔL is a negative number since investing in safety lowers the size of a loss, so that L₁ <L₀.)
Self-insurance involves spending S to change the size of a loss by ΔL (lowered from L₀ to L₁), for a loss with probability p.

How to Effectively Make a Prevention Decision

Determine the cost of the safety investment, S.
Estimate probability (p) and loss (L) with and without the investment: find p₀ & L₀ (without safety) and p₁ & L₁ (with safety).
Calculate expected loss: p × L, both without safety (p₀ × L₀) and with safety (p₁ × L₁).
Compute expected benefit of the safety investment, expected reduction in the expected loss due to the investment in safety: p₀ × L₀ - p₁ × L₁.
Compare expected benefit of the safety investment (p₀ × L₀ − p₁ × L₁, in Step 4) to cost of the safety investment (S, in Step 1)
Invest if and only if the cost S < expected benefit (p₀ × L₀ − p₁ × L₁).

For self-protection: expected benefit is Δp × L.
For self-insurance: expected benefit is p × ΔL.

Numeric Example: Bike Lock Decision (Marginal Analysis)

Bike value (L): $100

Options:

No lock: Probability of theft (p) = 50%, Cost = $0
Cheap lock: Probability of theft (p) = 5%, Cost = $10
Fancy lock: Probability of theft (p) = 1%, Cost = $30

Step 1: Compare Cheap Lock vs. No Lock

Marginal Cost (MC): $10 (cost of cheap lock)
Marginal Benefit (MB):
- Reduction in theft probability: 50% − 5% = 45%
- Expected loss avoided: 45% × $100 = $45
Decision: MB ($45) > MC ($10) → Buy the cheap lock ✓

Step 2: Compare Fancy Lock vs. Cheap Lock

Marginal Cost (MC): $20 (difference between fancy and cheap lock costs)
Marginal Benefit (MB):
- Reduction in theft probability: 5% − 1% = 4%
- Expected loss avoided: 4% × $100 = $4
Decision: MB ($4) < MC ($20) → Do NOT buy the fancy lock ✗

Conclusion: The cheap lock provides enough protection to justify its cost. The fancy lock is not worth the extra money compared to the cheap lock.

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