What is Probability❓
Probability = likelihood — possibility — chance of happening.
Probability distribution — gives possibility of each outcome of a random experiment — provides probabilities of different possible occurrences.
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)❓
Single weighted average ≡ long run average (mean) ≈ average result.
As if — same event (x) — take place repeatedly — thousands of times — ongoing basis — over a long run period of time.
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
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