Risk, Uncertainty and Decision Making: Expected Value, Decision Trees and Sensitivity Analysis (Basics) Questions

Question 1

Define risk.

Accepted Answer

**Risk** is a situation where outcomes are uncertain but **probabilities can be estimated**.

Question 2

Define uncertainty.

Accepted Answer

**Uncertainty** is a situation where outcomes are uncertain and **probabilities are not known reliably**.

Question 3

Write the formula for expected value (EV).

Accepted Answer

**EV = Σ (Outcome × Probability)**.

Question 4

What is EMV?

Accepted Answer

**EMV (Expected Monetary Value)** is the expected value of monetary outcomes computed using probabilities.

Question 5

What is a decision tree?

Accepted Answer

A **decision tree** is a diagram that shows **decisions and chance outcomes** in sequence.

Question 6

What is sensitivity analysis?

Accepted Answer

**Sensitivity analysis** studies how results change when **one assumption/variable** is changed at a time.

Question 7

Differentiate between risk and uncertainty.

Accepted Answer

**Risk** means outcomes are uncertain but **probabilities are known/estimable** using past data. **Uncertainty** means probabilities are **not known reliably**.

| Basis | **Risk** | **Uncertainty** |
|---|---|---|
| Probability | known/estimable | not known |
| Tools | **EMV**, decision trees | scenario planning, judgment |

Thus, risk is measurable; uncertainty is difficult to quantify.

Question 8

Explain expected value (EV) and its use in decisions.

Accepted Answer

**Expected value (EV)** is the weighted average of possible outcomes using probabilities.

**Formula:** **EV = Σ (Outcome × Probability)**.

**Use:** Under **risk**, EV/EMV helps compare alternatives and choose the one with highest expected payoff (especially for a **risk-neutral** manager).

EV is helpful but does not show risk spread.

Question 9

Explain risk attitudes: risk-averse, risk-neutral, risk-seeking.

Accepted Answer

- **Risk-averse**: prefers safer outcomes; may accept lower EMV for stability.
- **Risk-neutral**: chooses the alternative with highest **EMV**.
- **Risk-seeking**: prefers higher risk for higher possible gain.

Risk attitude affects the final decision even when EMV is known.

Question 10

Explain decision tree and rollback method (brief).

Accepted Answer

A **decision tree** shows decisions and chance events step-by-step.

**Rollback method:** compute expected values from the end branches backward by multiplying payoffs with probabilities and adding them at chance nodes, then choose the best branch at decision node.

It is useful for multi-stage decisions under risk.

Question 11

Explain sensitivity analysis and its importance.

Accepted Answer

**Sensitivity analysis** checks how results (profit/NPV) change when **one variable** changes while others remain constant.

**Importance:** it identifies **key risk drivers** (e.g., demand, price, cost) so managers focus on controlling or monitoring the most sensitive variables.

It improves decision robustness.

Question 12

Explain scenario analysis (brief) and how it differs from sensitivity analysis.

Accepted Answer

**Scenario analysis** evaluates combined changes in multiple variables under **best case, base case and worst case** scenarios.

**Sensitivity analysis** changes **one variable at a time**.

Scenario analysis is useful under uncertainty to see the overall impact of combined changes.

Question 13

Explain risk and uncertainty in managerial decisions. Differentiate them with a table and mention suitable tools.

Accepted Answer

**Risk** and **uncertainty** are common in managerial decision-making.

### 1) Meaning
- **Risk**: outcomes are uncertain but **probabilities are known/estimable**.
- **Uncertainty**: outcomes are uncertain and **probabilities cannot be assigned reliably**.

### 2) Difference (exam table)
| Basis | **Risk** | **Uncertainty** |
|---|---|---|
| Probability | known/estimable | not known |
| Data support | past data helps | limited/unreliable |
| Tools used | **EMV**, **decision tree** | **scenario planning**, judgment |

### 3) Managerial significance
- Under **risk**, managers can compute **Expected Value (EV/EMV)** and compare alternatives.
- Under **uncertainty**, managers use scenarios, flexibility and conservative planning.

Thus, risk can be measured to some extent, while uncertainty is harder to quantify.

Question 14

Explain EMV method with formula, steps and a simple example. Mention one limitation.

Accepted Answer

### **Expected Monetary Value (EMV)**
**EMV** is the weighted average of possible monetary outcomes using probabilities.

**Formula:**
- **EMV = Σ (Payoff × Probability)**

### Steps (flow)
```text
List alternatives → list outcomes + probabilities → compute EMV for each
→ choose highest EMV (risk-neutral)
```

### Simple example
Suppose Alternative A gives profit ₹1,00,000 with p=0.6 and loss ₹20,000 with p=0.4.
- **EMV(A) = 1,00,000×0.6 + (-20,000)×0.4 = 60,000 − 8,000 = ₹52,000**

### Limitation
EMV is an **average** and may ignore **variability** and worst-case outcomes, so risk attitude matters.

Question 15

Explain decision tree method and sensitivity analysis. Show steps/flow and a small table for sensitivity.

Accepted Answer

### **Decision tree**
A **decision tree** is a diagram showing decisions and chance events in sequence.

### Steps (rollback method)
1) Identify **decision alternatives** (decision node = square).
2) Add **chance outcomes** with probabilities (chance node = circle).
3) Write **payoffs** at end branches.
4) Compute **expected values backward** (rollback).
5) Choose the path with best value (as per objective/risk attitude).

```text
Square (Decision) → Circle (Chance) → Payoffs
             ← Rollback (compute EV backward)
```

### **Sensitivity analysis** (risk driver)
Sensitivity analysis tests how results change when **one variable** changes.

| Variable changed | Change | Result impact |
|---|---:|---|
| Demand | ±10% | profit changes a lot? |
| Price | ±5% | profit changes a lot? |

Managers focus on variables with the biggest impact (key risk drivers).

Basis	Risk	Uncertainty
Probability	known/estimable	not known
Tools	EMV, decision trees	scenario planning, judgment

Risk, Uncertainty and Decision Making: Expected Value, Decision Trees and Sensitivity Analysis (Basics)

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