Dean's Office Official Model Question Paper

Answer:

Answer:

• Macaulay Duration ($D_{\text{mac}}$): The weighted average term to maturity of a bond’s future cash flows (coupons and par), weighted by the present value of each cash flow:
  $$D_{\text{mac}} = \frac{\sum_{t=1}^n \frac{t \times CF_t}{(1 + y)^t}}{P_0}$$
• Modified Duration ($D_{\text{mod}}$): Direct measure of a bond’s percentage price volatility with respect to a 100-basis-point change in yield to maturity:
  $$\% \Delta P \approx -D_{\text{mod}} \times \Delta y$$

Mathematical Relationship:

$$D_{\text{mod}} = \frac{D_{\text{mac}}}{1 + \frac{y}{m}}$$

Where $y$ is annual YTM and $m$ is coupon compounding frequency per year.

Answer: Efficient Market Hypothesis (EMH): Asserts that financial asset prices fully, instantly, and accurately reflect all available relevant information, preventing investors from consistently achieving abnormal risk-adjusted returns.

Three Forms of Market Efficiency:

1. Weak-Form Efficiency: Current prices fully reflect all past market trading data (historical prices, trading volumes). Technical analysis cannot generate alpha.
2. Semi-Strong Form Efficiency: Prices instantaneously adjust to all publicly available information (financial statements, earnings releases, macroeconomic news). Fundamental analysis cannot generate alpha.
3. Strong-Form Efficiency: Prices reflect all information, both public and private insider information. Even corporate insiders cannot beat the market.

Answer:

• Sharpe Ratio: Evaluates excess return generated per unit of total risk: $S_p = \frac{R_p - R_f}{\sigma_p}$.
• Treynor Ratio: Evaluates excess return generated per unit of systematic risk: $T_p = \frac{R_p - R_f}{\beta_p}$.

When Treynor is Preferred: The Treynor Ratio is preferred when evaluating an investment portfolio that is part of a broader, well-diversified master fund (e.g., an institutional pension sub-allocation). In such a context, the fund’s unsystematic risk is diversified away by the master portfolio, making systematic risk ($\beta$) the only relevant risk metric.

Answer: Technical Analysis: An investment methodology that evaluates securities by analyzing statistical market patterns generated from historical price movements and trading volumes rather than intrinsic business financials.

• Support Level: A lower price threshold where concentrated buying interest is historically strong enough to absorb selling pressure, halting downward trends and providing a buy/long entry point.
• Resistance Level: An upper price ceiling where selling interest is strong enough to overwhelm buying demand, halting upward rallies and providing a sell/profit-taking exit point.

Solution: Markowitz Portfolio Theory & Minimum Variance Portfolio

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Step 1: Covariance Calculation

$$\sigma_X^2 = (18)^2 = 324\%^2, \quad \sigma_Y^2 = (30)^2 = 900\%^2$$

$$Cov(X, Y) = \rho_{XY} \times \sigma_X \times \sigma_Y = -0.20 \times 18 \times 30 = \mathbf{-108.0\%^2}$$

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Part (a): Weights of Minimum Variance Portfolio (MVP) (4 Marks)

$$w_X^* = \frac{\sigma_Y^2 - Cov(X, Y)}{\sigma_X^2 + \sigma_Y^2 - 2 Cov(X, Y)}$$

$$w_X^* = \frac{900 - (-108)}{324 + 900 - 2(-108)} = \frac{900 + 108}{1,224 + 216} = \frac{1,008}{1,440} = \mathbf{0.70 \text{ (or 70.0\%)}}$$

$$w_Y^* = 1 - w_X^* = 1 - 0.70 = \mathbf{0.30 \text{ (or 30.0\%)}}$$

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Part (b): Expected Return & Standard Deviation of MVP (3 Marks)

1. Expected Return of MVP:

$$E(R_{\text{mvp}}) = w_X^* E(R_X) + w_Y^* E(R_Y) = 0.70(16\%) + 0.30(24\%) = 11.2\% + 7.2\% = \mathbf{18.40\%}$$

2. Variance and Standard Deviation of MVP:

$$\sigma_{\text{mvp}}^2 = (w_X^*)^2 \sigma_X^2 + (w_Y^*)^2 \sigma_Y^2 + 2 w_X^* w_Y^* Cov(X, Y)$$

$$\sigma_{\text{mvp}}^2 = (0.70)^2(324) + (0.30)^2(900) + 2(0.70)(0.30)(-108)$$

$$\sigma_{\text{mvp}}^2 = (0.49)(324) + (0.09)(900) + (0.42)(-108) = 158.76 + 81.00 - 45.36 = 194.40\%^2$$

$$\sigma_{\text{mvp}} = \sqrt{194.40} = \mathbf{13.94\%}$$

Remarkable Analytical Finding: The portfolio standard deviation ($\sigma_{\text{mvp}} = 13.94\%$) is strictly lower than BOTH individual component assets ($\sigma_X = 18.0\%$ and $\sigma_Y = 30.0\%$). This is the mathematical signature of Markowitz portfolio diversification under negative correlation.

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Part (c): 50/50 Portfolio Comparison & Correlation Impact (3 Marks)

1. Expected Return of 50/50 Portfolio:

$$E(R_{50/50}) = 0.50(16\%) + 0.50(24\%) = 8.0\% + 12.0\% = \mathbf{20.00\%}$$

2. Standard Deviation of 50/50 Portfolio:

$$\sigma_{50/50}^2 = (0.50)^2(324) + (0.50)^2(900) + 2(0.50)(0.50)(-108)$$

$$\sigma_{50/50}^2 = (0.25)(324) + (0.25)(900) + (0.50)(-108) = 81.00 + 225.00 - 54.00 = 252.00\%^2$$

$$\sigma_{50/50} = \sqrt{252.00} = \mathbf{15.87\%}$$

3. Portfolio Comparison Table:

Diversification Commentary: Because $\rho_{XY} = -0.20 < 0$, the assets exhibit counter-cyclical movements. By combining 70% Stock X and 30% Stock Y, the investor achieves a higher return than Stock X alone ($18.4\% > 16.0\%$) while cutting total risk by over 4 percentage points below Stock X’s standalone risk ($13.94\% < 18.00\%$).

Solution: Security Market Line (SML) & Equity Valuation

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Part (a): SML Equation Formulation (2 Marks)

• Risk-Free Rate ($R_f$) = 5.0%
• Expected Market Return ($R_m$) = 13.0%
• Market Risk Premium ($MRP = R_m - R_f$) = $13.0\% - 5.0\% = \mathbf{8.0\%}$$\text{SML Equation: } k_i = R_f + \beta_i (R_m - R_f) = 5.0\% + \beta_i (8.0\%)$$

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Parts (b), (c), and (d): Required Returns, Alpha, Valuation & Recommendations (8 Marks)

Calculations:

1. Nabil Bank Ltd. (A):

   • Required Return ($k_A$) = $5.0\% + 0.80(8.0\%) = 5.0\% + 6.40\% = \mathbf{11.40\%}$
   • Jensen’s Alpha ($\alpha_A$) = Forecast Return - Required Return = $12.00\% - 11.40\% = \mathbf{+0.60\%}$
   • Status: Forecasted return exceeds required return ($\hat{R} > k \implies \alpha > 0$). Under-Valued.
   • Recommendation: BUY.

2. Upper Tamakoshi Hydro (B):

   • Required Return ($k_B$) = $5.0\% + 1.25(8.0\%) = 5.0\% + 10.00\% = \mathbf{15.00\%}$
   • Jensen’s Alpha ($\alpha_B$) = $14.50\% - 15.00\% = \mathbf{-0.50\%}$
   • Status: Forecasted return falls below required return ($\hat{R} < k \implies \alpha < 0$). Over-Valued.
   • Recommendation: SELL.

3. Himalayan Distillery (C):

   • Required Return ($k_C$) = $5.0\% + 1.60(8.0\%) = 5.0\% + 12.80\% = \mathbf{17.80\%}$
   • Jensen’s Alpha ($\alpha_C$) = $18.50\% - 17.80\% = \mathbf{+0.70\%}$
   • Status: Forecasted return exceeds required return ($\alpha > 0$). Under-Valued.
   • Recommendation: BUY.

4. Nepal Telecom (D):

   • Required Return ($k_D$) = $5.0\% + 0.50(8.0\%) = 5.0\% + 4.00\% = \mathbf{9.00\%}$
   • Jensen’s Alpha ($\alpha_D$) = $8.50\% - 9.00\% = \mathbf{-0.50\%}$
   • Status: Forecasted return falls below required return ($\alpha < 0$). Over-Valued.
   • Recommendation: SELL.

Comprehensive SML Evaluation Table:

Interpretation: Securities plotting above the SML generate positive alpha ($\alpha > 0$). Their current market prices are suppressed below their fundamental intrinsic values, offering excess risk-adjusted returns that warrant a BUY recommendation. Conversely, securities below the SML generate negative alpha and should be SOLD or avoided.

Solution: Bond Duration, Volatility & Immunization

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Part (a): Bond Price Computation at $y = 8\%$ (2 Marks)

• Par Value ($M$) = Rs. 10,000, Annual Coupon ($I$) = $10\% \times 10,000 = \text{Rs. } 1,000$
• Maturity ($n$) = 3 years, Yield to Maturity ($y$) = 8% = 0.08

$$P_0 = \frac{1,000}{(1.08)^1} + \frac{1,000}{(1.08)^2} + \frac{11,000}{(1.08)^3}$$

$$P_0 = 925.9259 + 857.3388 + 8,732.1643 = \mathbf{\text{Rs. } 10,515.43}$$

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Part (b): Macaulay Duration & Modified Duration (5 Marks)

1. Duration Calculation Schedule:

2. Macaulay Duration ($D_{\text{mac}}$):

$$D_{\text{mac}} = \frac{\sum t \times PV_t}{P_0} = \frac{28,837.0964}{10,515.4290} = \mathbf{2.742 \text{ years}}$$

3. Modified Duration ($D_{\text{mod}}$):

$$D_{\text{mod}} = \frac{D_{\text{mac}}}{1 + y} = \frac{2.74238}{1 + 0.08} = \frac{2.74238}{1.08} = \mathbf{2.539 \text{ years}}$$

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Part (c): Interest Rate Shock of +100 bps (+1.00%) (2 Marks)

• Yield Change ($\Delta y$) = $+1.00\% = +0.01$

1. Estimated Percentage Price Change:

$$\% \Delta P \approx -D_{\text{mod}} \times \Delta y = -2.5392 \times (+0.01) = -0.025392 = \mathbf{-2.539\%}$$

2. Estimated New Bond Price:

$$\text{New Price} \approx P_0 \times (1 + \% \Delta P) = 10,515.43 \times (1 - 0.025392) = \mathbf{\text{Rs. } 10,248.42}$$

(Note: Exact repricing at 9% gives $\frac{1,000}{1.09} + \frac{1,000}{(1.09)^2} + \frac{11,000}{(1.09)^3} = \text{Rs. } 10,253.13$. The minor Rs. 4.71 difference represents positive bond convexity).

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Part (d): Portfolio Immunization Mechanism (1 Mark)

Bond Immunization: A risk-management strategy where an institutional investor structures a fixed-income portfolio such that its Macaulay duration exactly matches the targeted investment planning horizon ($D_{\text{mac}} = H$). When interest rates fluctuate, the price risk (loss in capital value when rates rise) is exactly counterbalanced by reinvestment rate risk (higher interest earned on reinvested coupons), locking in the guaranteed target yield.

Solution: Fundamental Analysis & Two-Stage FCFE Valuation

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Part (a): Top-Down EIC Fundamental Analysis Framework (5 Marks)

The Top-Down EIC framework evaluates equity investments through three sequential analytical tiers:

1. Economic Analysis (E): Assesses macroeconomic climate to identify optimal market timing:
   • GDP Growth: Accelerating GDP expansion signals growing corporate revenues and higher aggregate corporate profits.
   • Interest Rates: Rising interest rates raise borrowing costs, compress corporate margins, and increase the equity discount rate ($k_e$), depressing equity valuations.
   • Inflation & Forex: High inflation erodes real consumer purchasing power; exchange rate depreciation increases import costs but boosts export competitiveness and remittance rupee value.
2. Industry Analysis (I): Identifies sectors positioned for above-average growth using Porter’s Five Forces (threat of entry, supplier power, buyer power, substitution, rivalry) and industry life-cycle stages (pioneering, expansion, maturity, decline).
3. Company Analysis (C): Examines individual corporate fundamentals through financial ratio analysis (profitability, liquidity, leverage, turnover) and competitive moats (brand equity, cost leadership, patents).

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Part (b): Two-Stage FCFE Valuation for Butwal Power Company (5 Marks)

1. Cost of Equity via CAPM:

• Risk-Free Rate ($R_f$) = 5.5%
• Stock Beta ($\beta$) = 1.10, Market Risk Premium ($MRP$) = 6.5%
  $$k_e = R_f + \beta(MRP) = 5.5\% + 1.10(6.5\%) = 5.5\% + 7.15\% = \mathbf{12.65\% = 0.1265}$$

2. Forecast Cash Flows during High-Growth Phase (Years 1 and 2 @ $g_1 = 25\%$):

• $FCFE_1 = FCFE_0(1 + g_1) = 30.00 \times (1 + 0.25) = \mathbf{\text{Rs. } 37.50}$
• $FCFE_2 = FCFE_1(1 + g_1) = 37.50 \times (1 + 0.25) = \mathbf{\text{Rs. } 46.875}$

3. Terminal Cash Flow & Terminal Value at Year 2 ($P_2$):

• First stable growth cash flow: $FCFE_3 = FCFE_2(1 + g_n) = 46.875 \times (1 + 0.06) = \text{Rs. } 49.6875$
• Terminal Horizon Value ($P_2$):
  $$P_2 = \frac{FCFE_3}{k_e - g_n} = \frac{49.6875}{0.1265 - 0.0600} = \frac{49.6875}{0.0665} = \mathbf{\text{Rs. } 747.1805}$$

4. Present Value of Cash Inflows & Intrinsic Value per Share ($P_0$):

• $PV(FCFE_1) = \frac{37.50}{(1 + 0.1265)^1} = \frac{37.50}{1.1265} = \text{Rs. } 33.2890$
• $PV(FCFE_2) = \frac{46.875}{(1 + 0.1265)^2} = \frac{46.875}{1.269002} = \text{Rs. } 36.9385$
• $PV(P_2) = \frac{747.1805}{(1 + 0.1265)^2} = \frac{747.1805}{1.269002} = \text{Rs. } 588.7938$$P_0 = PV(FCFE_1) + PV(FCFE_2) + PV(P_2) = 33.2890 + 36.9385 + 588.7938 = \mathbf{\text{Rs. } 659.02 \text{ per share}}$$

Conclusion: The intrinsic value of Butwal Power Company Ltd. is Rs. 659.02 per share.

Case Solution: Portfolio Performance Attribution & Risk-Adjusted Evaluation

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Part (a): Performance Metrics Computations (9 Marks)

Given: $R_f = 5.0\%, R_m = 14.0\%, \sigma_m = 18.0\%, \beta_m = 1.00$.

1. Sharpe Ratio ($S_p = \frac{R_p - R_f}{\sigma_p}$):

• Everest Fund: $S_{\text{Everest}} = \frac{22.0 - 5.0}{24.0} = \frac{17.0}{24.0} = \mathbf{0.7083}$
• Annapurna Fund: $S_{\text{Annapurna}} = \frac{16.5 - 5.0}{14.0} = \frac{11.5}{14.0} = \mathbf{0.8214}$
• NEPSE Benchmark: $S_{\text{NEPSE}} = \frac{14.0 - 5.0}{18.0} = \frac{9.0}{18.0} = \mathbf{0.5000}$

2. Treynor Ratio ($T_p = \frac{R_p - R_f}{\beta_p}$):

• Everest Fund: $T_{\text{Everest}} = \frac{22.0 - 5.0}{1.35} = \frac{17.0}{1.35} = \mathbf{12.593\%}$
• Annapurna Fund: $T_{\text{Annapurna}} = \frac{16.5 - 5.0}{0.85} = \frac{11.5}{0.85} = \mathbf{13.529\%}$
• NEPSE Benchmark: $T_{\text{NEPSE}} = \frac{14.0 - 5.0}{1.00} = \frac{9.0}{1.00} = \mathbf{9.000\%}$

3. Jensen’s Alpha ($\alpha_p = R_p - [R_f + \beta_p(R_m - R_f)]$):

• Everest Fund:
  $$\alpha_{\text{Everest}} = 22.0\% - [5.0\% + 1.35(14.0\% - 5.0\%)] = 22.0\% - [5.0\% + 12.15\%] = 22.0\% - 17.15\% = \mathbf{+4.85\%}$$
• Annapurna Fund:
  $$\alpha_{\text{Annapurna}} = 16.5\% - [5.0\% + 0.85(14.0\% - 5.0\%)] = 16.5\% - [5.0\% + 7.65\%] = 16.5\% - 12.65\% = \mathbf{+3.85\%}$$
• NEPSE Benchmark:
  $$\alpha_{\text{NEPSE}} = 14.0\% - [5.0\% + 1.00(14.0\% - 5.0\%)] = \mathbf{0.00\%}$$

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Part (b): Comparative Ranking & Discrepancy Analysis (5 Marks)

Explanation of Ranking Discrepancy:

1. Why Everest Wins on Jensen’s Alpha: Jensen’s Alpha measures absolute rupee/percentage outperformance over the CAPM required benchmark. Everest generated a massive raw return of 22.0%, outperforming its CAPM hurdle rate by +4.85% through aggressive stock-picking in high-beta sectors.
2. Why Annapurna Wins on Sharpe and Treynor: The Sharpe and Treynor ratios measure efficiency per unit of risk. Everest took on disproportionate risk ($\sigma = 24.0\%, \beta = 1.35$) to generate its return. Annapurna achieved an impressive 16.5% return with remarkably low volatility ($\sigma = 14.0\%$, lower than the market’s 18.0%). Annapurna is far more risk-efficient, delivering more excess return per unit of total risk and per unit of beta.

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Part (c): Modigliani-Modigliani ($M^2$) Measure (3 Marks)

$$M^2 = R_f + S_p \times \sigma_m$$

• Everest Fund:

  $$M^2_{\text{Everest}} = 5.0\% + 0.70833 \times 18.0\% = 5.0\% + 12.75\% = \mathbf{17.75\%}$$
  $$\text{Differential vs Market} = 17.75\% - 14.00\% = \mathbf{+3.75\%}$$

• Annapurna Fund:

  $$M^2_{\text{Annapurna}} = 5.0\% + 0.82143 \times 18.0\% = 5.0\% + 14.786\% = \mathbf{19.786\%}$$
  $$\text{Differential vs Market} = 19.786\% - 14.00\% = \mathbf{+5.786\%}$$

Retail Investor Interpretation: The $M^2$ measure scales each portfolio’s risk by borrowing or lending at the risk-free rate until its volatility equals benchmark market volatility (18.0%). If Annapurna were leveraged up to market risk, it would earn an astonishing 19.79% (beating the market by 5.79%). This clearly demonstrates to retail investors that Annapurna provides superior risk-adjusted wealth generation.

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Part (d): Targeted Investor Recommendations (3 Marks)

1. Conservative Retail Investor (Single-Fund Portfolio):
   • Recommendation: Annapurna Balanced Value Fund.
   • Rationale: For an investor committing their entire wealth to one fund, total risk ($\sigma$) cannot be diversified away. Annapurna offers the highest Sharpe ratio (0.8214) and highest $M^2$ (19.79%), providing stable returns with volatility well below the market index (14% vs 18%).
2. Institutional Provident Fund (Satellite Allocation):
   • Recommendation: Everest Aggressive Growth Fund.
   • Rationale: The institutional investor already owns a broadly diversified core portfolio that eliminates unsystematic risk. In an active satellite allocation, the sole objective is maximizing pure alpha. Everest generates the highest Jensen’s Alpha (+4.85%), making it the ideal vehicle for active alpha generation.