Fundamentals of Investment 2078 Board Question Paper

Four Investment Vehicles Available in Nepal

1. Common Stocks: Listed corporate equities traded continuously on NEPSE.
2. Mutual Funds: SEBON-regulated open-ended and closed-ended collective investment schemes.
3. Government Treasury Bills and Development Bonds: Issued by NRB for risk-free income.
4. Corporate Debentures: Fixed-coupon debt securities issued by commercial banks.

Definition of Primary Market

The primary market is the original issue market where corporate enterprises and governments sell newly created securities directly to initial investors to raise fresh investment capital for physical and business expansion.

Why We Compute a Market Index

1. Performance Benchmark: Evaluates whether portfolio managers outperform general market averages.
2. Economic Barometer: Gauges overall macroeconomic sentiment and investor confidence.
3. Asset Pricing & Risk Factor: Serves as the proxy for the market portfolio return ($R_m$) in CAPM.

Definition of Systematic Risk

Systematic risk (market risk or undiversifiable risk) is the variability in security returns caused by macroeconomic factors affecting the entire economy (inflation, GDP growth, interest rate shifts, geopolitical events). Measured by Beta ($\beta$), it cannot be eliminated through portfolio diversification.

Concept of Short Sale

A short sale is an investment transaction wherein an investor borrows shares of stock from a brokerage firm and sells them on the open market, expecting the stock price to decline so they can buy back identical shares later at a lower price to return to the lender.

Estimation of Net Profit for 2020:

• Projected Sales 2020 = $\text{Rs. } 83,650,000$
• Projected Net Profit Margin = $8\% = 0.08$$\text{Net Profit} = \text{Sales} \times \text{Net Profit Margin} = 83,650,000 \times 0.08 = \mathbf{\text{Rs. } 6,692,000}$$ Conclusion: Estimated net profit for 2020 is Rs. 6,692,000.

Calculation of Conversion Value:

• Conversion Ratio ($CR$) = 20
• Common Stock Market Price ($P_0$) = $\text{Rs. } 49$$\text{Conversion Value} = CR \times P_0 = 20 \times 49 = \mathbf{\text{Rs. } 980}$$ Conclusion: The bond’s conversion value is Rs. 980.

Offer Price of Mutual Fund Shares:

• Net Asset Value ($NAV$) = $\text{Rs. } 15$
• Front-end Load Fee = $5\% = 0.05$$\text{Offer Price} = \frac{NAV}{1 - \text{Load Fee}} = \frac{15}{1 - 0.05} = \frac{15}{0.95} = \mathbf{\text{Rs. } 15.79}$$ Conclusion: The offering price is Rs. 15.79 per share.

CAPM Required Return and Purchase Decision:

• Risk-free Rate ($R_f$) = $6\%$, Market Return ($R_m$) = $12\%$, Beta ($\beta$) = $1.5$$E(R_i) = R_f + \beta [R_m - R_f] = 6\% + 1.5 [12\% - 6\%] = 6\% + 9\% = \mathbf{15.0\%}$$ Recommendation: YES, purchase the stock. Since the expected return (16.0%) exceeds the CAPM required return (15.0%), the stock is undervalued and yields positive alpha.

Value of Put Option:

• Strike Price ($X$) = $\text{Rs. } 145$
• Market Price ($S$) = $\text{Rs. } 135$$\text{Value of Put} = \max(0, X - S) = \max(0, 145 - 135) = \mathbf{\text{Rs. } 10}$$ Conclusion: The intrinsic value of the put option is Rs. 10.

Role of Investment Bankers in Securities Offering

An investment banker (merchant banker) is a licensed financial intermediary that specializes in raising long-term capital for corporate and institutional clients.

Major Roles:

1. Origination & Structuring: Designing security structures, prospectus drafting, and legal compliance with SEBON.
2. Underwriting (Risk Bearing): Guaranteeing the purchase of unsold issue shares, insulating issuers from market failure.
3. Pricing & Valuation: Determining fair issue pricing and optimal subscription timing.
4. Distribution & Syndication: Mobilizing institutional and retail investor networks via C-ASBA.

Percentage Return on Margin Purchase (100 shares at Rs 150):

• Total Purchase Cost $= 100 \times 150 = \text{Rs. } 15,000$.

• Initial Margin $= 60\% \implies$ Initial Equity $= 15,000 \times 0.60 = \text{Rs. } 9,000$.

• Margin Loan $= 15,000 - 9,000 = \text{Rs. } 6,000$. Price rises to $\text{Rs. } 175$.

• a. Return on Margin Investment (No dividends/interest):

  $$\text{Capital Gain} = 100(175 - 150) = \text{Rs. } 2,500$$
  $$\text{Return on Equity} = \frac{2,500}{9,000} = 0.2778 = \mathbf{27.78\%}$$

• b. Return with Dividend Rs 15 and Loan Interest 10%:

  • Dividends Received $= 100 \times 15 = \text{Rs. } 1,500$.
  • Interest on Loan $= 6,000 \times 10\% = \text{Rs. } 600$.
  • Net Profit $= 2,500 + 1,500 - 600 = \text{Rs. } 3,400$.
    $$\text{Return on Equity} = \frac{3,400}{9,000} = 0.3778 = \mathbf{37.78\%}$$

• c. Effect of Commissions: Brokerage commissions paid upon buying and selling increase initial cash outlay and reduce net proceeds, thereby lowering overall return on equity.

Price-Weighted vs. Value-Weighted Index Analysis:

Given: Stock A (Rs 200, 1M shares), B (Rs 800, 0.2M shares), C (Rs 400, 0.25M shares). Stock B splits 2-for-1 at end of 2018.

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a. Price-Weighted Index (PWI):

• 2018 Base PWI: $\frac{200 + 800 + 400}{3} = \frac{1,400}{3} = \mathbf{466.67}$.
• Divisor Adjustment for Stock B Split: Price of B drops to Rs 400.
  $$\text{New Divisor } (d) = \frac{200 + 400 + 400}{466.67} = \frac{1,000}{466.67} = \mathbf{2.142857}$$
• 2019 PWI: Prices are A = 250, B = 420, C = 450.
  $$PWI_{2019} = \frac{250 + 420 + 450}{2.142857} = \frac{1,120}{2.142857} = \mathbf{522.67}$$
  $$\text{Rate of Return} = \frac{522.67 - 466.67}{466.67} = \mathbf{12.00\%}$$

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b. Value-Weighted Index (VWI):

• 2018 Market Cap: $(200 \times 1\text{M}) + (800 \times 0.2\text{M}) + (400 \times 0.25\text{M}) = 200\text{M} + 160\text{M} + 100\text{M} = \mathbf{\text{Rs. } 460\text{M}}$.
• 2019 Market Cap: $(250 \times 1\text{M}) + (420 \times 0.4\text{M}) + (450 \times 0.25\text{M}) = 250\text{M} + 168\text{M} + 112.5\text{M} = \mathbf{\text{Rs. } 530.5\text{M}}$.
  $$\text{Rate of Return} = \frac{530.5\text{M} - 460\text{M}}{460\text{M}} = \frac{70.5}{460} = \mathbf{15.33\%}$$

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c. Why the Returns Differ:

PWI weights stocks purely by share price (high-priced stocks dominate), whereas VWI weights stocks by total market capitalization (large market-cap firms dominate).

Bond Duration and Interest Rate Sensitivity Analysis:

• Par Value = $\text{Rs. } 1,000$, Maturity = 3 years, Coupon = $7\%$, Sells at par (Rs 1,000).

• a. Yield to Maturity (YTM): Since the bond sells at par, $YTM = \text{Coupon Rate} = \mathbf{7.0\%}$.

• b. Macaulay Duration ($D$):

  • Year 1: $PV(70) = 70 / 1.07 = 65.42 \implies t \times PV = 65.42$
  • Year 2: $PV(70) = 70 / (1.07)^2 = 61.14 \implies t \times PV = 122.28$
  • Year 3: $PV(1070) = 1070 / (1.07)^3 = 873.44 \implies t \times PV = 2,620.32$$D = \frac{65.42 + 122.28 + 2,620.32}{1,000} = \frac{2,808.02}{1,000} = \mathbf{2.808 \text{ years}}$$

• c. Modified Duration ($D^*$):

  $$D^* = \frac{D}{1 + y} = \frac{2.808}{1.07} = \mathbf{2.624 \text{ years}}$$

• d. Percentage Price Change if Yield Rises to 7.5% ($\Delta y = +0.005$):

  $$\% \Delta P \approx -D^* \times \Delta y = -2.624 \times (+0.005) = -0.01312 = \mathbf{-1.31\%}$$

Sahara Closed-End Fund HPR Analysis:

• One Year Ago: $NAV_0 = \text{Rs. } 10.50$, Discount = $10\% \implies P_0 = 10.50(0.90) = \text{Rs. } 9.45$.

• Today: $NAV_1 = \text{Rs. } 12.00$, Premium = $5\% \implies P_1 = 12.00(1.05) = \text{Rs. } 12.60$.

• Annual Distribution = $\text{Rs. } 1.50$.

• a. NAV-Based HPR:

  $$HPR_{\text{NAV}} = \frac{NAV_1 - NAV_0 + D}{NAV_0} = \frac{12.00 - 10.50 + 1.50}{10.50} = \frac{3.00}{10.50} = \mathbf{28.57\%}$$

• b. Market-Based HPR:

  $$HPR_{\text{Market}} = \frac{P_1 - P_0 + D}{P_0} = \frac{12.60 - 9.45 + 1.50}{9.45} = \frac{4.65}{9.45} = \mathbf{49.21\%}$$
  Conclusion: The shift from a $10\%$ discount to a $5\%$ premium significantly added value to the investor, generating a market return ($49.21\%$) that exceeded fund asset performance ($28.57\%$) by 20.64%.

Performance Evaluation of Banking Equity Fund:

Given: Fund Return = $12\%$, $\sigma = 20\%$, $\beta = 0.6$. NEPSE = $14\%$, $\sigma = 15\%$, $\beta = 1.0$. $R_f = 6\%$.

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a. Portfolio Performance Metrics:

1. Sharpe Ratio ($S_p = \frac{R_p - R_f}{\sigma_p}$):
   • Fund: $\frac{12 - 6}{20} = \mathbf{0.30}$
   • NEPSE: $\frac{14 - 6}{15} = \mathbf{0.533}$
2. Treynor Ratio ($T_p = \frac{R_p - R_f}{\beta_p}$):
   • Fund: $\frac{12 - 6}{0.6} = \mathbf{10.0\%}$
   • NEPSE: $\frac{14 - 6}{1.0} = \mathbf{8.0\%}$
3. Jensen’s Alpha ($\alpha_p = R_p - [R_f + \beta_p(R_m - R_f)]$):
   $$\alpha = 12 - [6 + 0.6(14 - 6)] = 12 - [6 + 4.8] = 12 - 10.8 = \mathbf{+1.20\%}$$

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b. Performance Conclusion:

Treynor’s measure and Jensen’s Alpha showed that the Equity Fund outperformed the market (Treynor $10.0\% > 8.0\%$, Alpha $+1.20\%$). The Sharpe ratio underperformed because the banking sector portfolio was concentrated and bore high unsystematic risk.

Economic Cycle Phases, Asset Allocation, and Nepalese Investment Environment

1. Economic Cycle Phases:
   • Expansion: Strong GDP growth, rising profits. Strategy: Overweight equities and cyclicals.
   • Peak: High inflation, rising interest rates. Strategy: Shift to commodities and floating debt.
   • Contraction / Recession: Falling corporate profits. Strategy: Overweight long-term government bonds.
   • Trough: Low interest rates and nascent recovery. Strategy: Accumulate undervalued equities.
2. Investment Environment in Nepal:
   • Regulated by SEBON and NRB; computerized demat trading via CDSC and Meroshare.
   • High dominance of banking and hydropower sectors; limited institutional derivatives.

Comprehensive Analysis of Investment Alternatives A, B, and C:

• Probability: Recession ($0.2$), Normal ($0.3$), Boom ($0.5$).

• Equity Fund A: $E(R_A) = (0.2 \times 8) + (0.3 \times 10) + (0.5 \times 12) = 1.6 + 3.0 + 6.0 = \mathbf{10.6\%}$. $\beta_A = 1.0$.

• Stock B: $E(R_B) = (0.2 \times 6) + (0.3 \times 12) + (0.5 \times 15) = 1.2 + 3.6 + 7.5 = \mathbf{12.3\%}$. $\beta_B = 1.2$.

• CD C: Constant $7\% \implies E(R_C) = \mathbf{7.0\%}$, $\sigma_C = 0$, $\beta_C = 0$.

• a. Highest Expected Return: Stock B provides the highest expected return (12.3%).

• b. Risk Measures:

  • Standard Deviation: Certificate of Deposit C is least risky ($\sigma_C = 0\%$).
  • Beta: Stock B is most risky ($\beta = 1.2$).

• c. Portfolio Risk Comparisons:

  • Portfolio X (75% A, 25% B): $\beta_X = (0.75 \times 1.0) + (0.25 \times 1.2) = \mathbf{1.05}$.
  • Portfolio Y (50% B, 50% C): $\beta_Y = (0.50 \times 1.2) + (0.50 \times 0) = \mathbf{0.60}$.
  • Conclusion: Portfolio Y is least risky in terms of both standard deviation and beta.

Mero Nepal Company Dividend Valuation:

Given: $D_0 = \text{Rs. } 30$, Growth $= 10\%$ for 3 years, then $6\%$ perpetually. $R_f = 5\%$, $R_m = 14\%$, $\beta = 1.4$.

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a. Required Rate of Return ($k_s$):

$$k_s = R_f + \beta(R_m - R_f) = 5\% + 1.4(14\% - 5\%) = 5\% + 12.6\% = \mathbf{17.6\%}$$

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b. Maximum Price Willing to Pay ($V_0$):

• $D_1 = 30(1.10) = \text{Rs. } 33.00$
• $D_2 = 33(1.10) = \text{Rs. } 36.30$
• $D_3 = 36.30(1.10) = \text{Rs. } 39.93$
• $D_4 = 39.93(1.06) = \text{Rs. } 42.326$
• Horizon Price at Year 3:
  $$P_3 = \frac{D_4}{k_s - g} = \frac{42.326}{0.176 - 0.06} = \frac{42.326}{0.116} = \text{Rs. } 364.88$$
  $$V_0 = \frac{33}{1.176} + \frac{36.30}{(1.176)^2} + \frac{39.93 + 364.88}{(1.176)^3} = 28.06 + 26.25 + \frac{404.81}{1.62645} = 28.06 + 26.25 + 248.89 = \mathbf{\text{Rs. } 303.20}$$

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c. Dividend Yield and Capital Gain Yield in Year 4:

In constant growth stage, Capital Gain Yield = $g = \mathbf{6.0\%}$, and Dividend Yield = $k_s - g = 17.6\% - 6.0\% = \mathbf{11.6\%}$.

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d. Zero Growth After Year 3 ($g = 0$):

$$P_3^* = \frac{D_3}{k_s} = \frac{39.93}{0.176} = \text{Rs. } 226.875$$

$$V_0^* = 28.06 + 26.25 + \frac{39.93 + 226.875}{1.62645} = 54.31 + \frac{266.805}{1.62645} = 54.31 + 164.04 = \mathbf{\text{Rs. } 218.35}$$