02.07.03 |【03】| Use of “Probabilities (ρ) and Expected Values (EV)”

What is Probability❓

ℹ Probability = likelihood — possibility — chance of happening.


ℹ Probability distribution — gives possibility of each outcome of a random experiment — provides probabilities of different possible occurrences.


ℹ Applications in various sectors — make future predictions based on a sample for a random experiment — e.g. in business — predict if profit or loss to the company using any new strategy.

What is Expected Value (EV)❓

ℹ Single weighted average ≡ long run average (mean) ≈ average result.


ℹ As if — same event (x) — take place repeatedly — thousands of times — ongoing basis — over a long run period of time.


ℹ As opposed to one-off situation — either 100% profit or 100% loss — where expected value (EV) may be misleading.

Be mindful ⚠

ℹ Take note : actual ≠ expectation — therefore — expected value (EV) ≠ most likely outcome ≠ possible result — not to be mistaken.


ℹ Outcome — highest probability = most likely outcome = possible result.


ℹ Actual outcome — actual result — may below OR above EV (expectation).

How to measure EV❓

ℹ Using formula.


ℹ Formula ▼


EV = ∑px


where :


p = probability of the outcome occurring (chances of happening)


x = future outcome e.g. cash flow $

What about risk profile of decision makers❓ Does it matter❓

ℹ Yes — absolutely — different risk-return attitude — influence decision making outcome.


ℹ Risk profile :


1️⃣ risk-taking person


2️⃣ risk-avoiding person


3️⃣ risk indifferent person – don’t bothering risk


ℹ Take risk — risk seeker — go for best possible outcomes (higher payoff) but less certainty — apply “Maximax” approach — high risk high return — bet the best outcome to happen.


ℹ Avoid risk — risk averse — go for lower possible outcome (lower payoff) but more certainty — apply “Maximin” or “Minimax” approach — low risk low return.


ℹ Don’t bother risk — risk neutral — indifferent in risk — only focus on return — regardless degree of risk — consider all possible outcomes — go for highest payoff.


ℹ Thought-provoking : Which one should be the priority concern?


🤔 Risk? Return?


🤔 Return then Risk?


🤔 Risk then Return?


🤔 Only Risk?


🤔 Only Return?

What are the benefits of using expected values❓

Some of the benefits | advantages :


ℹ Identify calculated risk — probability of each possible outcome — expected value.


ℹ Reduced information — easier decisions.


ℹ Calculations — relatively simple.

What are the limitations of expected values❓

Some of the limitations | disadvantages :


ℹ Probabilities — subjective.


ℹ EV — merely a weighted average — little meaning for a one-off project.


ℹ EV gives no indication of the dispersion of possible outcomes about the EV, i.e. the risk.


ℹ EV – not correspond – not relatable – to any of the actual possible outcomes.

How Utility Theory influence decision making❓

ℹ Risk attitude — depend on the amount of money involved — BIG deal [V.S] small deal.



ℹ Imagine two separate proposals ▼ which to accept or reject❓


1️⃣ Bet on the toss of a coin — if heads — win $6 — otherwise — lose $4.


2️⃣ Bet on the toss of a coin — if heads — win $6,000 — otherwise — lose $4,000.


ℹ For average person — scenario 2️⃣ riskier than 1️⃣ — due to BIG sums of money — no bother probabilities — ignoring range of possible outcomes — therefore might…


✅ Accept 1️⃣


❎ Reject 2️⃣