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Dean's Office Official Model Question Paper

FIN 253 · Fundamentals of Investment

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Programme
BBS
Academic year
Fourth Year
Paper type
Official Model Question
Sitting
Dean's Office Blueprint
Full marks
100
Duration
180 minutes

Tribhuvan University

Faculty of Management

Office of the Dean

Official Model Question Paper / Dean's Office Blueprint

Course: FIN 253 · Fundamentals of Investment

Level: Bachelor of Business Studies (BBS) · Fourth Year

Full Marks: 100

Time: 3 hrs.

Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.

Group 'A'

Brief Answer Questions. Attempt ALL questions.

[10 × 2 = 20]
  1. Define Investment and contrast it with Speculation on the basis of time horizon and risk.

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    Answer: Investment: The commitment of current funds into financial or real assets for a long-term period in anticipation of receiving future cash flows that compensate for time, expected inflation, and risk, based on thorough fundamental analysis. Contrast with Speculation:

    • Time Horizon: Investment focuses on medium-to-long-term horizons; speculation seeks quick gains over short-term price fluctuations.
    • Risk Profile: Investors take calculated, moderate risk supported by asset value; speculators take high, aggressive risks driven by market rumors or momentum.
  2. What is the Security Market Line (SML)? Write its equation.

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    Answer: Security Market Line (SML): The graphical representation of the Capital Asset Pricing Model (CAPM) depicting the linear relationship between expected return and systematic risk (measured by Beta, β\beta) for individual assets or portfolios. Equation:

    E(Ri)=Rf+βi[E(Rm)Rf]E(R_i) = R_f + \beta_i [E(R_m) - R_f]
    Where RfR_f is risk-free rate, E(Rm)E(R_m) is expected market return, and [E(Rm)Rf][E(R_m) - R_f] is market risk premium.

  3. Distinguish between Systematic Risk and Unsystematic Risk with one example of each.

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    Answer:

    • Systematic (Market) Risk: Non-diversifiable risk stemming from macroeconomic factors that impact all securities simultaneously (e.g., nationwide inflation spikes, central bank interest rate hikes, political upheaval).
    • Unsystematic (Company-Specific) Risk: Unique, diversifiable risk caused by microeconomic factors specific to an individual firm or industry (e.g., labor strike at a factory, product recall, CEO resignation).
  4. Define the Beta Coefficient (β\beta) of a security. What does β=1.4\beta = 1.4 signify?

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    Answer: Beta (β\beta): A standardized measure of a security’s sensitivity or volatility relative to movements in the overall market portfolio:

    βi=Cov(Ri,Rm)σm2\beta_i = \frac{\text{Cov}(R_i, R_m)}{\sigma_m^2}

    Meaning of β=1.4\beta = 1.4: The stock is 40% more volatile than the market benchmark. If the market index (NEPSE) rises by 10%, the stock is expected to gain 14%; if the market declines by 10%, the stock is expected to fall by 14%.

  5. What is the Macaulay Duration of a bond?

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    Answer: Macaulay Duration: The weighted average term to maturity of the cash flows from a bond, where the weights are the present values of each respective cash flow relative to the total bond price:

    D=t=1nt×PV(CFt)PriceD = \sum_{t=1}^{n} \frac{t \times \text{PV}(\text{CF}_t)}{\text{Price}}

    It quantifies both the effective maturity and the interest rate price sensitivity of the bond.

  6. An equity analyst estimates the following probability distribution for Stock A: Boom (Probability = 0.60, Return = 22%), Recession (Probability = 0.40, Return = -8%). Calculate the Expected Return and Variance.

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    Solution:

    1. Expected Return:
      E(R)=(0.60×22%)+(0.40×8%)=13.2%3.2%=10.0%E(R) = (0.60 \times 22\%) + (0.40 \times -8\%) = 13.2\% - 3.2\% = \mathbf{10.0\%}
    2. Variance (σ2\sigma^2):
      σ2=Pi[RiE(R)]2=0.60(2210)2+0.40(810)2\sigma^2 = \sum P_i [R_i - E(R)]^2 = 0.60(22 - 10)^2 + 0.40(-8 - 10)^2
      σ2=0.60(144)+0.40(324)=86.4+129.6=216.0%2    σ=216=14.70%\sigma^2 = 0.60(144) + 0.40(324) = 86.4 + 129.6 = \mathbf{216.0\%^2} \implies \sigma = \sqrt{216} = \mathbf{14.70\%}
  7. State the three forms of the Efficient Market Hypothesis (EMH) formulated by Eugene Fama.

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    Answer:

    1. Weak Form: Stock prices fully reflect all past trading history and historical price/volume data (Technical analysis cannot generate abnormal returns).
    2. Semi-Strong Form: Stock prices adjust rapidly to all publicly available information, including financial statements, earnings announcements, and macroeconomic news (Fundamental analysis cannot earn abnormal returns).
    3. Strong Form: Stock prices reflect all information, public and private/insider information alike (Nobody, even corporate insiders, can earn abnormal returns).
  8. Differentiate between an Open-End Mutual Fund and a Closed-End Mutual Fund in Nepal.

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    Answer:

    • Open-End Mutual Fund: Has no fixed maturity and variable capital; units are bought and sold directly through the fund manager at daily Net Asset Value (NAV).
    • Closed-End Mutual Fund: Has a fixed maturity (e.g., 7 or 10 years) and fixed number of units; listed and traded on the stock exchange (NEPSE) between investors, often trading at a discount or premium to NAV.
  9. Define Margin Trading and distinguish between Initial Margin and Maintenance Margin.

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    Answer: Margin Trading: Buying securities by borrowing a portion of the purchase price from a broker/bank using the purchased securities as collateral.

    • Initial Margin: The minimum percentage of equity cash that the investor must deposit upfront at the time of purchasing the stock (e.g., 50%).
    • Maintenance Margin: The minimum equity percentage that the investor must maintain in the margin account after purchase before triggering a margin call.
  10. What is Technical Analysis? Name any two commonly used technical indicators.

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    Answer: Technical Analysis: A security analysis methodology that forecasts future price movements and trends based on historical price charts, trading volume, and market behavioral patterns rather than company intrinsic financials. Two Common Indicators:

    1. Relative Strength Index (RSI): A momentum oscillator measuring overbought (>70) and oversold (<30) conditions.
    2. Moving Average Convergence Divergence (MACD): A trend-following momentum indicator displaying relationship between two moving averages.

Group 'B'

Descriptive Answer Questions. Attempt any FIVE questions.

[5 × 10 = 50]
  1. An investor holds a portfolio of two stocks: Stock A and Stock B. The statistical data are:

    • Stock A: Expected Return E(RA)=14%E(R_A) = 14\%, Standard Deviation σA=18%\sigma_A = 18\%, Weight wA=0.60w_A = 0.60.
    • Stock B: Expected Return E(RB)=20%E(R_B) = 20\%, Standard Deviation σB=26%\sigma_B = 26\%, Weight wB=0.40w_B = 0.40.

    Required: (a) Compute the Portfolio Expected Return E(Rp)E(R_p). (b) Compute the Portfolio Standard Deviation σp\sigma_p under three distinct scenarios: 1. Perfect Positive Correlation (ρAB=+1.0\rho_{AB} = +1.0) 2. Zero Correlation (ρAB=0.0\rho_{AB} = 0.0) 3. Perfect Negative Correlation (ρAB=1.0\rho_{AB} = -1.0) (c) What fundamental principle of Markowitz Portfolio Theory does this demonstrate?

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    Solution: Markowitz Two-Asset Portfolio Analysis


    Part (a): Portfolio Expected Return

    E(Rp)=wAE(RA)+wBE(RB)=(0.60×14%)+(0.40×20%)=8.4%+8.0%=16.40%E(R_p) = w_A E(R_A) + w_B E(R_B) = (0.60 \times 14\%) + (0.40 \times 20\%) = 8.4\% + 8.0\% = \mathbf{16.40\%}

    (Expected return is a linear weighted average unaffected by correlation).


    Part (b): Portfolio Standard Deviation

    The portfolio variance equation is:

    σp=wA2σA2+wB2σB2+2wAwBσAσBρAB\sigma_p = \sqrt{w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2 w_A w_B \sigma_A \sigma_B \rho_{AB}}

    • wA2σA2=(0.60)2(18)2=0.36×324=116.64w_A^2 \sigma_A^2 = (0.60)^2 (18)^2 = 0.36 \times 324 = 116.64
    • wB2σB2=(0.40)2(26)2=0.16×676=108.16w_B^2 \sigma_B^2 = (0.40)^2 (26)^2 = 0.16 \times 676 = 108.16
    • 2wAwBσAσB=2(0.60)(0.40)(18)(26)=224.642 w_A w_B \sigma_A \sigma_B = 2(0.60)(0.40)(18)(26) = 224.64

    1. Scenario 1: ρAB=+1.0\rho_{AB} = +1.0 (Perfect Positive Correlation)

    σp=116.64+108.16+224.64(1.0)=449.44=21.20%\sigma_p = \sqrt{116.64 + 108.16 + 224.64(1.0)} = \sqrt{449.44} = \mathbf{21.20\%}

    (Note: Exactly equal to weighted average: 0.60(18)+0.40(26)=10.8+10.4=21.20%0.60(18) + 0.40(26) = 10.8 + 10.4 = 21.20\%. No risk diversification).

    2. Scenario 2: ρAB=0.0\rho_{AB} = 0.0 (Zero Correlation / Independent)

    σp=116.64+108.16+0=224.80=14.99%\sigma_p = \sqrt{116.64 + 108.16 + 0} = \sqrt{224.80} = \mathbf{14.99\%}

    (Portfolio risk drops below both individual stocks’ weighted average and even below Stock A’s individual risk!).

    3. Scenario 3: ρAB=1.0\rho_{AB} = -1.0 (Perfect Negative Correlation)

    σp=116.64+108.16224.64=0.16=0.40%0%\sigma_p = \sqrt{116.64 + 108.16 - 224.64} = \sqrt{0.16} = \mathbf{0.40\%} \approx \mathbf{0\%}

    Part (c): Fundamental Markowitz Diversification Principle

    This demonstrates that portfolio risk is driven fundamentally by the correlation coefficient (ρ\rho) between assets, not merely individual asset risks.

    • When correlation is less than +1.0+1.0, diversification eliminates unsystematic risk without sacrificing portfolio expected return.
    • When correlation reaches 1.0-1.0, risk can be virtually eliminated while still achieving a lucrative 16.4% expected return.
  2. The risk-free rate of return (RfR_f) is 5% and the expected return on the market portfolio (RmR_m) is 13%. You are evaluating three stocks on NEPSE:

    Stock Beta (β\beta) Estimated Return (RR)
    Stock X 0.80 12.0%
    Stock Y 1.00 13.0%
    Stock Z 1.40 15.0%

    Required: (a) Compute the Required Rate of Return for each stock using the CAPM. (b) Calculate Jensen’s Alpha (α\alpha) for each stock. (c) State which stocks are Overpriced, Underpriced, or Fairly Priced, and advise an investor whether to buy, hold, or sell.

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    Solution: CAPM Security Valuation


    Part (a) & (b): Computations under CAPM

    Market Risk Premium =E(Rm)Rf=13%5%=8%= E(R_m) - R_f = 13\% - 5\% = 8\%. CAPM Required Return: ki=Rf+βi[E(Rm)Rf]=5%+βi(8%)k_i = R_f + \beta_i [E(R_m) - R_f] = 5\% + \beta_i(8\%). Jensen’s Alpha: αi=Estimated Return (Ri)Required Return (ki)\alpha_i = \text{Estimated Return } (R_i) - \text{Required Return } (k_i).

    Stock Beta (beta\\beta) Estimated Return (RiR_i) Required Return (kik_i) Alpha (alpha\\alpha) Valuation Status Investment Decision
    X 0.80 12.0% 5%+0.80(8%)=11.4%5\% + 0.80(8\%) = \mathbf{11.4\%} +0.60%+0.60\% Underpriced (Lies above SML) BUY
    Y 1.00 13.0% 5%+1.00(8%)=13.0%5\% + 1.00(8\%) = \mathbf{13.0\%} 0.00%0.00\% Fairly Priced (Lies on SML) HOLD
    Z 1.40 15.0% 5%+1.40(8%)=16.2%5\% + 1.40(8\%) = \mathbf{16.2\%} 1.20%-1.20\% Overpriced (Lies below SML) SELL

    Part (c): Strategic Evaluation

    • Stock X (Alpha = +0.60%): Generates an expected return (12.0%) higher than its required risk-adjusted benchmark (11.4%). Its current price is too low; investors should BUY Stock X.
    • Stock Y (Alpha = 0.00%): Accurately priced for its systematic market risk; investors should HOLD.
    • Stock Z (Alpha = -1.20%): Offers only 15.0% return while requiring 16.2% for its high systematic risk (β=1.4\beta = 1.4). Its market price is inflated; investors should SELL or short-sell Stock Z.
  3. Sanima Bank Ltd. issues a 6-year, Rs. 1,000 par value bond with an 8% coupon rate payable semi-annually. The current market price of the bond is Rs. 950.

    Required: (a) Compute the Current Yield of the bond. (b) Compute the Nominal Yield to Maturity (YTM) using the approximation formula. (c) Calculate the Effective Annual Yield (EAY) of the bond.

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    Solution: Semi-Annual Bond Valuation


    Given:

    • Par Value (MM): Rs. 1,000
    • Annual Coupon Rate: 8%     \implies Annual Coupon =Rs. 80= \text{Rs. } 80
    • Semi-annual Coupon (C/2C/2): 802=Rs. 40\frac{80}{2} = \text{Rs. } 40
    • Current Market Price (V0V_0): Rs. 950
    • Maturity (nn): 6 years     \implies Semi-annual periods (2n2n) = 12 periods

    Part (a): Current Yield

    Current Yield=Annual Coupon PaymentCurrent Market Price=Rs. 80Rs. 950=8.42%\text{Current Yield} = \frac{\text{Annual Coupon Payment}}{\text{Current Market Price}} = \frac{\text{Rs. } 80}{\text{Rs. } 950} = \mathbf{8.42\%}

    Part (b): Approximate Yield to Maturity (YTM)

    For semi-annual payments, let semi-annual yield be YTMsemiYTM_{semi}:

    YTMsemi(C/2)+MV02nM+2V03=40+1,000950121,000+2(950)3YTM_{semi} \approx \frac{(C/2) + \frac{M - V_0}{2n}}{\frac{M + 2V_0}{3}} = \frac{40 + \frac{1,000 - 950}{12}}{\frac{1,000 + 2(950)}{3}}
    Numerator=40+5012=40+4.167=44.167\text{Numerator} = 40 + \frac{50}{12} = 40 + 4.167 = 44.167
    Denominator=1,000+1,9003=2,9003=966.67\text{Denominator} = \frac{1,000 + 1,900}{3} = \frac{2,900}{3} = 966.67
    YTMsemi44.167966.67=0.04569=4.569% per six monthsYTM_{semi} \approx \frac{44.167}{966.67} = 0.04569 = 4.569\% \text{ per six months}
    Nominal Annual YTM=2×YTMsemi=2×4.569%=9.138%9.14%\mathbf{\text{Nominal Annual YTM}} = 2 \times YTM_{semi} = 2 \times 4.569\% = \mathbf{9.138\% \approx 9.14\%}

    Part (c): Effective Annual Yield (EAY)

    EAY=(1+YTMsemi)21=(1+0.04569)21=(1.04569)21=1.093471=9.35%\mathbf{\text{EAY}} = (1 + YTM_{semi})^2 - 1 = (1 + 0.04569)^2 - 1 = (1.04569)^2 - 1 = 1.09347 - 1 = \mathbf{9.35\%}
  4. Explain the Two-Stage (Supernormal) Dividend Discount Model. A growth company recently paid a dividend (D0D_0) of Rs. 10 per share. It is projected to experience supernormal growth of 20% per year for the next 3 years, after which the growth rate will settle to a stable 6% indefinitely. The investor’s required rate of return is 14%. Compute the Intrinsic Value of the stock.

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    Solution: Two-Stage Dividend Discount Valuation


    Given:

    • Current Dividend (D0D_0): Rs. 10.00
    • Supernormal Growth Rate (gsg_s): 20% (for Years 1 to 3)
    • Stable Long-term Growth Rate (gng_n): 6% (from Year 4 onward)
    • Required Rate of Return (kek_e): 14% (0.140.14)

    Step 1: Forecast Dividends during Supernormal Period (Years 1–3)

    • D1=D0(1+gs)=10×(1+0.20)=Rs. 12.00D_1 = D_0(1 + g_s) = 10 \times (1 + 0.20) = \text{Rs. } 12.00
    • D2=D1(1+gs)=12×(1+0.20)=Rs. 14.40D_2 = D_1(1 + g_s) = 12 \times (1 + 0.20) = \text{Rs. } 14.40
    • D3=D2(1+gs)=14.40×(1+0.20)=Rs. 17.28D_3 = D_2(1 + g_s) = 14.40 \times (1 + 0.20) = \text{Rs. } 17.28

    Step 2: Present Value of Supernormal Dividends at ke=14%k_e = 14\%

    • PV(D1)=12.00(1.14)1=12.001.14=Rs. 10.53PV(D_1) = \frac{12.00}{(1.14)^1} = \frac{12.00}{1.14} = \text{Rs. } 10.53
    • PV(D2)=14.40(1.14)2=14.401.2996=Rs. 11.08PV(D_2) = \frac{14.40}{(1.14)^2} = \frac{14.40}{1.2996} = \text{Rs. } 11.08
    • PV(D3)=17.28(1.14)3=17.281.48154=Rs. 11.66PV(D_3) = \frac{17.28}{(1.14)^3} = \frac{17.28}{1.48154} = \text{Rs. } 11.66Total PV of Dividends (Years 1–3)=10.53+11.08+11.66=Rs. 33.27\text{Total PV of Dividends (Years 1–3)} = 10.53 + 11.08 + 11.66 = \mathbf{\text{Rs. } 33.27}$

    Step 3: Compute Terminal Stock Price (P3P_3) at End of Year 3

    First, determine D4D_4 under stable growth (gn=6%g_n = 6\%):

    D4=D3(1+gn)=17.28×(1+0.06)=Rs. 18.3168D_4 = D_3(1 + g_n) = 17.28 \times (1 + 0.06) = \text{Rs. } 18.3168
    P3=D4kegn=18.31680.140.06=18.31680.08=Rs. 228.96P_3 = \frac{D_4}{k_e - g_n} = \frac{18.3168}{0.14 - 0.06} = \frac{18.3168}{0.08} = \mathbf{\text{Rs. } 228.96}


    Step 4: Present Value of Terminal Price (P3P_3)

    PV(P3)=P3(1.14)3=228.961.48154=Rs. 154.54PV(P_3) = \frac{P_3}{(1.14)^3} = \frac{228.96}{1.48154} = \mathbf{\text{Rs. } 154.54}

    Step 5: Total Intrinsic Value of the Stock (P0P_0)

    P0=PV of Dividends (1–3)+PV(P3)=Rs. 33.27+154.54=Rs. 187.81\mathbf{P_0} = \text{PV of Dividends (1–3)} + PV(P_3) = \text{Rs. } 33.27 + 154.54 = \mathbf{\text{Rs. } 187.81}
  5. Explain the E-I-C (Economy-Industry-Company) Framework of Fundamental Analysis. How should an equity research analyst apply this framework when selecting equities on NEPSE?

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    1. The Top-Down E-I-C Valuation Framework

    Fundamental analysis follows a hierarchical top-down approach to determine whether an equity is fundamentally sound and fairly valued.

                      [ 1. Economic Analysis ]
                      - GDP, Remittance, Interest Rates, Inflation
                                 |
                                 v
                      [ 2. Industry Analysis ]
                      - Industry Life Cycle, Regulations, Porter's Forces
                                 |
                                 v
                      [ 3. Company Analysis ]
                      - Financial Statements, Management, Governance, Competitive Moat
    

    2. Application to NEPSE Stock Selection

    A. Economic Analysis (Macro Environment)

    • Monetary Policy & Liquidity: Bank liquidity directly dictates stock market cycles. In Nepal, when the banking sector experiences a liquidity crunch and interbank rates jump to 8%–10%, equity valuations contract. When liquidity is flush and interest rates plunge, equity markets rally.
    • Remittance Inflows: Surging worker remittances stimulate household disposable income, driving consumption and capital market retail investments.

    B. Industry Analysis (Sector Selection)

    • Identify sectors poised to benefit from current economic conditions:
      • Hydropower Sector: Benefit from government power purchase agreements (PPA) and export treaties with India.
      • Commercial Banks: Mergers reducing overheads, though constrained by asset quality and loan-loss provisions.
      • Tourism/Hospitality: Expanding post-crisis tourism arrivals in Pokhara, Chitwan, and Kathmandu.

    C. Company Analysis (Firm Selection)

    • Financial Statement Ratios: Evaluate Return on Equity (ROE), Net Interest Margin (NIM), Non-Performing Loans (NPL ratio), Price-to-Earnings (P/E) multiple, and Price-to-Book (P/B) ratio.
    • Management Integrity & Corporate Governance: Evaluate promoter reputation, transparency in quarterly reporting, and consistency in dividend payout track records.

    Conclusion: Buying a great company operating in a collapsing industry during a macroeconomic recession leads to losses. The E-I-C framework ensures that capital is deployed only when economic tailwinds, industry strength, and firm-level superiority align.

  6. Explain the three classic Portfolio Performance Evaluation Measures: Sharpe’s Ratio, Treynor’s Ratio, and Jensen’s Alpha. When is Sharpe’s ratio preferred over Treynor’s ratio?

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    1. The Three Portfolio Performance Measures

                         Portfolio Performance Metrics
                                       |
         +-----------------------------+-----------------------------+
         |                             |                             |
    Sharpe Ratio                 Treynor Ratio                 Jensen's Alpha
    Total Risk Benchmark (sigma) Systematic Risk Benchmark (beta) Abnormal Return vs SML
    

    A. Sharpe Ratio (SpS_p)

    Measures the excess return earned per unit of Total Risk (standard deviation, σp\sigma_p):

    Sp=RˉpRfσpS_p = \frac{\bar{R}_p - R_f}{\sigma_p}

    • Evaluates the steepness of the Capital Allocation Line (CAL).
    • Higher Sharpe ratio indicates superior risk-adjusted performance.

    B. Treynor Ratio (TpT_p)

    Measures the excess return earned per unit of Systematic Risk (beta, βp\beta_p):

    Tp=RˉpRfβpT_p = \frac{\bar{R}_p - R_f}{\beta_p}

    • Assumes the portfolio is already completely diversified, so unsystematic risk has been eliminated.

    C. Jensen’s Alpha (αp\alpha_p)

    Measures the absolute abnormal return generated by the fund manager over and above the return predicted by the CAPM:

    αp=Rˉp[Rf+βp(RˉmRf)]\alpha_p = \bar{R}_p - [R_f + \beta_p (\bar{R}_m - R_f)]

    • If α>0\alpha > 0: Manager demonstrated superior stock selection and market timing skill.
    • If α<0\alpha < 0: Manager underperformed the benchmark.

    2. When to Use Sharpe vs. Treynor

    • Use Sharpe Ratio: When evaluating an investor’s entire wealth portfolio (or when the portfolio is poorly diversified). Since total risk (σ\sigma) encompasses both systematic and unsystematic risk, Sharpe rewards proper diversification.
    • Use Treynor Ratio: When evaluating a specific mutual fund that will be added as a small component to an already well-diversified macro portfolio. Here, unique risk will be diversified away, so only systematic risk (β\beta) matters.

Group 'C'

Analytical Answer Questions. Attempt any TWO questions.

[2 × 15 = 30]
  1. An institutional investment committee is analyzing two risky assets, Asset X and Asset Y, to construct an optimal portfolio:

    • Asset X: E(RX)=12%,σX=16%E(R_X) = 12\%, \sigma_X = 16\%
    • Asset Y: E(RY)=20%,σY=24%E(R_Y) = 20\%, \sigma_Y = 24\%
    • The correlation coefficient between the returns of Asset X and Asset Y is ρXY=0.20\rho_{XY} = -0.20.
    • The risk-free borrowing and lending rate (RfR_f) is 6%.

    Required: (a) Compute the portfolio weights (wXw_X and wYw_Y) that constitute the Minimum Variance Portfolio (MVP) and calculate its expected return and standard deviation. (6 Marks) (b) Calculate the expected return and standard deviation of a portfolio containing 60% in Asset X and 40% in Asset Y. (4 Marks) (c) Define the Capital Allocation Line (CAL) and explain why risk-averse investors select different points along the CAL while investing in the identical optimal risky tangency portfolio. (5 Marks)

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    Solution: Markowitz Portfolio Optimization


    Part (a): Minimum Variance Portfolio (MVP) Formulation

    For a two-asset portfolio, the weight of Asset X that minimizes total portfolio variance is:

    wX=σY2Cov(X,Y)σX2+σY22Cov(X,Y)w_X^* = \frac{\sigma_Y^2 - \text{Cov}(X, Y)}{\sigma_X^2 + \sigma_Y^2 - 2 \text{Cov}(X, Y)}

    Where:

    • σX2=(16)2=256\sigma_X^2 = (16)^2 = 256
    • σY2=(24)2=576\sigma_Y^2 = (24)^2 = 576
    • Cov(X,Y)=ρXYσXσY=(0.20)×16×24=76.80\text{Cov}(X, Y) = \rho_{XY} \sigma_X \sigma_Y = (-0.20) \times 16 \times 24 = -76.80

    Substitute into the formula:

    wX=576(76.80)256+5762(76.80)=576+76.80832+153.60=652.80985.60=0.6623    66.23%w_X^* = \frac{576 - (-76.80)}{256 + 576 - 2(-76.80)} = \frac{576 + 76.80}{832 + 153.60} = \frac{652.80}{985.60} = \mathbf{0.6623 \implies 66.23\%}
    wY=1wX=10.6623=0.3377    33.77%w_Y^* = 1 - w_X^* = 1 - 0.6623 = \mathbf{0.3377 \implies 33.77\%}

    Expected Return of MVP:

    E(RMVP)=wXE(RX)+wYE(RY)=(0.6623×12%)+(0.3377×20%)E(R_{\text{MVP}}) = w_X^* E(R_X) + w_Y^* E(R_Y) = (0.6623 \times 12\%) + (0.3377 \times 20\%)
    E(RMVP)=7.948%+6.754%=14.70%E(R_{\text{MVP}}) = 7.948\% + 6.754\% = \mathbf{14.70\%}

    Standard Deviation of MVP:

    σMVP2=wX2σX2+wY2σY2+2wXwYCov(X,Y)\sigma_{\text{MVP}}^2 = w_X^2 \sigma_X^2 + w_Y^2 \sigma_Y^2 + 2 w_X w_Y \text{Cov}(X, Y)
    σMVP2=(0.6623)2(256)+(0.3377)2(576)+2(0.6623)(0.3377)(76.80)\sigma_{\text{MVP}}^2 = (0.6623)^2(256) + (0.3377)^2(576) + 2(0.6623)(0.3377)(-76.80)
    σMVP2=(0.4386×256)+(0.1140×576)34.364=112.28+65.6634.36=143.58%2\sigma_{\text{MVP}}^2 = (0.4386 \times 256) + (0.1140 \times 576) - 34.364 = 112.28 + 65.66 - 34.36 = 143.58\%^2
    σMVP=143.58=11.98%\sigma_{\text{MVP}} = \sqrt{143.58} = \mathbf{11.98\%}

    (Notice that the MVP risk of 11.98% is substantially lower than both Asset X’s 16% and Asset Y’s 24%!).


    Part (b): Portfolio with wX=0.60w_X = 0.60 and wY=0.40w_Y = 0.40

    1. Expected Return:
      E(Rp)=(0.60×12%)+(0.40×20%)=7.2%+8.0%=15.20%E(R_p) = (0.60 \times 12\%) + (0.40 \times 20\%) = 7.2\% + 8.0\% = \mathbf{15.20\%}
    2. Variance & Standard Deviation:
      σp2=(0.60)2(256)+(0.40)2(576)+2(0.60)(0.40)(76.80)\sigma_p^2 = (0.60)^2(256) + (0.40)^2(576) + 2(0.60)(0.40)(-76.80)
      σp2=(0.36×256)+(0.16×576)36.864=92.16+92.1636.86=147.46%2\sigma_p^2 = (0.36 \times 256) + (0.16 \times 576) - 36.864 = 92.16 + 92.16 - 36.86 = 147.46\%^2
      σp=147.46=12.14%\sigma_p = \sqrt{147.46} = \mathbf{12.14\%}

    Part (c): Capital Allocation Line (CAL) and Two-Fund Separation

    • Definition of CAL: The graphical line created by plotting expected return against risk (standard deviation) for all possible combinations of the risk-free asset (RfR_f) and an optimal risky portfolio (PP^*).
    • Slope of CAL: Represents the Sharpe Ratio of the optimal tangency portfolio:
      Slope (S)=E(RP)RfσP\text{Slope } (S) = \frac{E(R_{P^*}) - R_f}{\sigma_{P^*}}
    • Tobin’s Separation Theorem: The portfolio choice problem separates into two independent decisions:
      1. Technical Investment Decision: Identifying the unique optimal risky tangency portfolio (PP^*) which maximizes the Sharpe ratio. This portfolio is identical for all investors regardless of risk aversion.
      2. Financing / Personal Preference Decision: Choosing the proportion allocated to risk-free lending versus risky portfolio PP^* based on individual risk tolerance (utility indifference curves). Highly conservative investors hold mostly RfR_f and little PP^*; aggressive investors borrow at RfR_f to leverage portfolio PP^*.
  2. A corporate debenture of Nepal Telecom Ltd. has a face value of Rs. 1,000, carries an annual coupon rate of 9%, and matures in exactly 4 years. The current yield to maturity (YTM) on the debenture is 10%.

    Required: (a) Compute the Current Market Price (P0P_0) of the debenture. (3 Marks) (b) Calculate the Macaulay Duration (DD) and Modified Duration (DD^*) of the debenture. (6 Marks) (c) Using the Modified Duration approximation, estimate the Percentage Price Change and New Bond Price if market yields immediately drop by 150 basis points (-1.50%). (3 Marks) (d) Calculate the Exact Actual Price of the bond at the new YTM of 8.50%. Compare this with your duration-estimated price and explain why the duration rule underestimates bond price increases when interest rates fall (Convexity Effect). (3 Marks)

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    Solution: Bond Duration, Volatility, and Convexity


    Part (a): Current Market Price at YTM = 10%

    • Annual Coupon (CC): Rs. 1,000×9%=Rs. 90\text{Rs. } 1,000 \times 9\% = \text{Rs. } 90
    • Par Value (MM): Rs. 1,000; Maturity (nn): 4 years; y=10%y = 10\% (0.100.10)
    P0=90×PVIFA10%,4+1,000×PVIF10%,4P_0 = 90 \times \text{PVIFA}_{10\%, 4} + 1,000 \times \text{PVIF}_{10\%, 4}
    PVIFA10%,4=3.16987,PVIF10%,4=0.68301\text{PVIFA}_{10\%, 4} = 3.16987, \quad \text{PVIF}_{10\%, 4} = 0.68301
    P0=(90×3.16987)+(1,000×0.68301)=285.29+683.01=Rs. 968.30P_0 = (90 \times 3.16987) + (1,000 \times 0.68301) = 285.29 + 683.01 = \mathbf{\text{Rs. } 968.30}

    Part (b): Macaulay Duration (DD) and Modified Duration (DD^*)

    Year (tt) Cash Flow (CFtCF_t) Discount Factor (1.10)t(1.10)^{-t} PV of Cash Flow t×PV(CFt)t \times \text{PV}(CF_t)
    1 Rs. 90 0.90909 Rs. 81.82 Rs. 81.82
    2 Rs. 90 0.82645 Rs. 74.38 Rs. 148.76
    3 Rs. 90 0.75131 Rs. 67.62 Rs. 202.86
    4 Rs. 1,090 0.68301 Rs. 744.48 Rs. 2,977.92
    Total Rs. 968.30 Rs. 3,411.36
    Macaulay Duration (D)=t×PV(CFt)P0=Rs. 3,411.36Rs. 968.30=3.523 Years\mathbf{\text{Macaulay Duration } (D)} = \frac{\sum t \times \text{PV}(CF_t)}{P_0} = \frac{\text{Rs. } 3,411.36}{\text{Rs. } 968.30} = \mathbf{3.523 \text{ Years}}
    Modified Duration (D)=D1+y=3.5231+0.10=3.5231.10=3.203 Years\mathbf{\text{Modified Duration } (D^*)} = \frac{D}{1 + y} = \frac{3.523}{1 + 0.10} = \frac{3.523}{1.10} = \mathbf{3.203 \text{ Years}}

    Part (c): Duration-Estimated Price Change for Δy=1.50%\Delta y = -1.50\% (-0.015)

    %ΔPD×Δy=3.203×(0.015)=+0.04804=+4.80%\%\Delta P \approx -D^* \times \Delta y = -3.203 \times (-0.015) = +0.04804 = \mathbf{+4.80\%}
    Estimated Price Increase=Rs. 968.30×4.804%=Rs. 46.52\text{Estimated Price Increase} = \text{Rs. } 968.30 \times 4.804\% = \text{Rs. } 46.52
    Estimated New Bond Price=Rs. 968.30+46.52=Rs. 1,014.82\mathbf{\text{Estimated New Bond Price}} = \text{Rs. } 968.30 + 46.52 = \mathbf{\text{Rs. } 1,014.82}

    Part (d): Exact Bond Price at YTM = 8.50% and Convexity Explanation

    At new yield y=8.50%y = 8.50\% (0.0850.085):

    • PVIFA8.5%,4=1(1.085)40.085=3.2753\text{PVIFA}_{8.5\%, 4} = \frac{1 - (1.085)^{-4}}{0.085} = 3.2753
    • PVIF8.5%,4=(1.085)4=0.72157\text{PVIF}_{8.5\%, 4} = (1.085)^{-4} = 0.72157Actual P0=(90×3.2753)+(1,000×0.72157)=294.78+721.57=Rs. 1,016.35\text{Actual } P_0' = (90 \times 3.2753) + (1,000 \times 0.72157) = 294.78 + 721.57 = \mathbf{\text{Rs. } 1,016.35}$
      Actual Percentage Change=1,016.35968.30968.30=48.05968.30=+4.96%\text{Actual Percentage Change} = \frac{1,016.35 - 968.30}{968.30} = \frac{48.05}{968.30} = \mathbf{+4.96\%}

    Comparison & Convexity Explanation:

    • Duration estimated price =Rs. 1,014.82= \text{Rs. } 1,014.82 (+4.80%+4.80\%)
    • Actual market price =Rs. 1,016.35= \text{Rs. } 1,016.35 (+4.96%+4.96\%)
    • The duration rule underestimates the price increase by Rs. 1.53 because duration is a linear tangent approximation of a curved function. The price-yield relationship of a standard option-free bond is convex (curving upward).
    • When interest rates decline, Convexity works in favor of bondholders: prices rise faster than linear duration predicts, and when rates rise, prices fall slower than duration predicts.
  3. Critically analyze the Behavioral Biases observed among retail investors on the Nepal Stock Exchange (NEPSE). Evaluate how cognitive errors—such as Herd Behavior, Disposition Effect, Overconfidence, and Framing—fuel market speculative bubbles and subsequent crashes in Nepal, and suggest regulatory measures for investor protection.

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    1. The Behavioral Finance Revolution in Emerging Markets

    Traditional finance assumes market participants are fully rational, risk-averse utility maximizers who process all market information instantaneously. In contrast, Behavioral Finance integrates cognitive psychology to explain why actual market prices deviate systematically from intrinsic fundamental values due to psychological biases and irrational decision heuristics.


    2. Major Behavioral Biases Prevalent on NEPSE

                      Behavioral Anomalies Observed on NEPSE
                                        |
        +-------------------+-----------+-----------+-------------------+
        |                   |                       |                   |
    Herd Behavior &        Disposition Effect       Overconfidence &    Anchoring &
    Social Media Hype      & Loss Aversion          Illusion of Skill   Framing Bias
    

    1. Herd Behavior (Bhedi Bheda Chal)

    • In Nepal, retail investors heavily follow anonymous social media groups (Viber, Facebook stock chatrooms, Clubhouse) and prominent market speculators.
    • Retailers aggressively buy low-cap microfinance and hydropower stocks without examining debt burdens or audited balances merely because everyone else is buying, creating speculative price bubbles disconnected from fundamentals.

    2. The Disposition Effect (Mental Accounting & Loss Aversion)

    • Propounded by Shefrin and Statman: Investors rush to sell winning stocks prematurely to lock in modest gains ("greed for small profit"), while stubbornly holding onto deeply losing stocks for years hoping they will break even.
    • This creates severe capital misallocation, leaving retail portfolios dominated by financially distressed companies.

    3. Overconfidence and Self-Attribution Bias

    • During bull markets (e.g., NEPSE rising toward 3,200 index levels), beginner investors misattribute market-wide gains to their personal investment genius.
    • Overconfident investors borrow heavily via margin lending and cooperative loans to amplify positions, making them vulnerable when liquidity tightens.

    4. Gambler’s Fallacy & Lottery Preference

    • Intense retail obsession with 10-unit IPO applications and Right Shares (Hakprada), regardless of corporate fundamentals. Retailers treat right share offerings as "free bonus gifts" rather than equity dilution.

    3. Impact on Market Volatility in Nepal

    These synchronized cognitive biases create extreme price distortion:

    • Unprofitable hydropower entities with negative net worth have traded at P/E multiples exceeding 100$\times$.
    • When liquidity contracts, panic-selling takes hold; herd sentiment reverses completely, triggering limit-down circuit breakers and wiping out billions in household savings.

    4. Regulatory and Policy Interventions for SEBON and NEPSE

    Strategic Reform Concrete Implementation Measures
    Expansion of Institutional Investment Encourage institutional asset managers, pension funds, mutual funds, and market makers to dilute retail herd dominance and provide counter-cyclical price stabilization.
    Financial Literacy and Mandatory Risk Warnings Require broker TMS screens to display prominent risk disclosure pop-ups on high-volatility, low-float penny stocks with negative net worth or under regulatory monitoring.
    Crackdown on Illegal Market Manipulation Prosecute unauthorized financial influencers ("finfluencers"), pump-and-dump cartels, and unauthorized paid stock-tip groups under strict anti-market manipulation statutes.
    Dynamic Circuit Breakers and Price Bands Review individual stock circuit breaker limits to prevent coordinated cornering of illiquid scripts.

    5. Conclusion

    A resilient capital market requires both structural institutional modernization and investor behavioral maturity. By empowering SEBON’s surveillance mechanisms and fostering an investment culture rooted in fundamental cash flows rather than speculative gossip, Nepal can transform NEPSE into a trusted engine for national capital formation.