Investment Analysis

False. Commercial paper is an unsecured short-term promissory note issued by creditworthy corporations (and financial institutions), not by Nepal Rastra Bank. Nepal Rastra Bank issues instruments such as treasury-bill auctions on behalf of the government and its own bonds.

True. The holding period return is $\frac{10{,}000-9{,}600}{9{,}600}=\frac{400}{9{,}600}=4.166\%$ for the 65 days until maturity.

False. The maintenance margin is the minimum equity percentage that must be maintained in a margin account. If equity falls below it, the broker issues a margin call.

True. A value-weighted (market-capitalisation-weighted) index weights each stock by its market value, that is, price per share multiplied by the number of shares outstanding, so larger companies have more influence.

True. Blue chip stocks belong to large, financially sound, well-known companies with a long record of stable earnings and regular dividends.

False. A back-end load is a redemption (exit) fee charged when an investor sells or redeems fund shares, not when buying them. The fee charged at purchase is a front-end load.

False. The optimal risky portfolio is the combination of risky assets only, the one with the highest Sharpe ratio, where the capital allocation line is tangent to the efficient frontier. Combining it with the risk-free asset gives the optimal complete portfolio.

True. A bond indenture is the legal contract between the bond issuer and the bondholders (usually represented by a trustee). It sets out the coupon, maturity, collateral, covenants and other terms.

False. The price-earnings ratio is a valuation (market) ratio showing how much investors pay per rupee of earnings. Liquidity is measured by ratios such as the current ratio and quick ratio.

False. Municipal bonds are issued by local governments (municipalities) and not by the federal government. The federal government issues development bonds, treasury bills and national savings bonds.

(a) Without margin

$\text{Return}=\frac{100-80}{80}=25\%$

(b) With margin

Per share, the investor puts in $80\times 50\% =$ Rs 40 and borrows Rs 40.

(i) Margin call price. Let $P$ be the price at which equity equals 30% of the value: $\frac{P-40}{P}=0.30 \;\Rightarrow\; P=\frac{40}{0.70}=\text{Rs }57.14$ A margin call occurs if the price falls to about Rs 57.14.

(ii) Rate of return at Rs 100

• Interest on the loan: $40\times 9\% =$ Rs 3.60
• Net proceeds: $100-40-3.60=$ Rs 56.40
• Profit: $56.40-40=$ Rs 16.40

$\text{Return}=\frac{16.40}{40}=41\%$

Margin raises the return from 25% to 41%, but increases the risk.

Investment: Rs 10,000; NAV = Rs 10.

(a) Shares obtained

• Fund A (price = NAV = Rs 10, plus 2% commission): cost per share $=10\times1.02=$ Rs 10.20, so shares $=10{,}000/10.20=\mathbf{980.39}$.
• Fund B (20% discount, price Rs 8, plus 2% commission): cost per share $=8\times1.02=$ Rs 8.16, so shares $=10{,}000/8.16=\mathbf{1{,}225.49}$.
• Fund D (net load 8.54% on NAV): cost per share $=10\times1.0854=$ Rs 10.854, so shares $=10{,}000/10.854=\mathbf{921.3}$.
• Fund C (front-end load; the rate is not stated, so assume 8% of the offering price): net invested $=10{,}000\times0.92=9{,}200$, so shares $=9{,}200/10=\mathbf{920}$.

(b) Choice

Fund B gives the most shares (about 1,225) for the same Rs 10,000 because it is bought at a 20% discount to NAV, and the commission is only 2%. Each share still represents Rs 10 of assets, so Fund B should be purchased, assuming the discount does not widen. Funds C and D lose about 8.5% of the investment to loads, and Fund A loses 2%.

Assumptions: coupons received are reinvested at 7% (the rate available on the new bond), and the total of the proceeds is reinvested.

Years 1-2 (10% bond): coupons Rs 100 each year; the bond is called at the end of year 2 at Rs 1,160.

• At the end of year 2, funds in hand: $1{,}160+100=$ Rs 1,260, which buy 1.26 units of the new 7% bond.
• The first coupon (Rs 100 received at year 1) is reinvested at 7% for the remaining 4 years: $100(1.07)^4=\text{Rs }131.08$

Years 3-5 (7% bond): with coupons reinvested at 7%, the Rs 1,260 grows to $1{,}260(1.07)^3=1{,}260\times1.2250=\text{Rs }1{,}543.55$

Terminal value at year 5: $131.08+1{,}543.55=$ Rs 1,674.63

$\text{Actual YTM}=\left(\frac{1{,}674.63}{1{,}000}\right)^{1/5}-1=1.1086-1\approx \mathbf{10.86\%}$

The realised yield is slightly above the original 10% coupon because of the call premium, reduced somewhat by the lower reinvestment rate.

(a) Expected returns

$E(R_A)=0.1(-10)+0.2(5)+0.4(10)+0.2(25)+0.1(35)=12.5\%$ $E(R_B)=0.1(-20)+0.2(0)+0.4(15)+0.2(30)+0.1(40)=14.0\%$

(b) Standard deviations

Alpha deviations: $-22.5,\,-7.5,\,-2.5,\,12.5,\,22.5$ $\sigma_A^2=0.1(506.25)+0.2(56.25)+0.4(6.25)+0.2(156.25)+0.1(506.25)=146.25$ $\sigma_A=\sqrt{146.25}=12.09\%$

Beta deviations: $-34,\,-14,\,1,\,16,\,26$ $\sigma_B^2=0.1(1156)+0.2(196)+0.4(1)+0.2(256)+0.1(676)=274$ $\sigma_B=\sqrt{274}=16.55\%$

(c) Coefficient of variation

$CV_A=\frac{12.09}{12.5}=0.97,\qquad CV_B=\frac{16.55}{14.0}=1.18$

Alpha Bank has the lower risk per unit of return, so Alpha Bank's stock is preferred, even though Beta has a higher expected return.

Plowback $b=2/3$, so the payout is $1/3$. Growth $g=ROE\times b=9\%\times\frac{2}{3}=6\%$.

Required return (CAPM): $k=6\%+1.25(14\%-6\%)=16\%$.

(a) Price

$D_0=3\times\frac13=$ Rs 1, so $D_1=1(1.06)=$ Rs 1.06. $P_0=\frac{D_1}{k-g}=\frac{1.06}{0.16-0.06}=\text{Rs }10.60$

(b) P/E ratio

$E_1=3(1.06)=$ Rs 3.18 $\frac{P_0}{E_1}=\frac{10.60}{3.18}=3.33$ On current earnings (Rs 3), $P/E_0 = 3.53$.

(c) PVGO

$PVGO=P_0-\frac{E_1}{k}=10.60-\frac{3.18}{0.16}=10.60-19.875=-\text{Rs }9.275$

PVGO is negative because the ROE (9%) is below the required return (16%). The firm reinvests earnings at a rate lower than investors require, so growth destroys value.

Role of the stock market

• Mobilises savings: it channels the savings of households into productive long-term investment in companies.
• Capital raising: firms raise equity through IPOs, FPOs and rights issues, and the government and companies raise debt.
• Liquidity: investors can convert shares into cash easily on the secondary market.
• Price discovery: continuous trading sets fair prices that reflect information about firms.
• Corporate governance and discipline: listed firms must disclose information and are monitored by investors and the regulator.
• Wealth creation and risk sharing: investors share in company profits and diversify risk.
• Economic indicator: the market index reflects the health of the economy.
• Facilitates privatisation and investment opportunities for foreign and institutional investors.

Current status of the Nepalese stock market

• The Nepal Stock Exchange (NEPSE) is the only stock exchange, operating under the Securities Board of Nepal (SEBON), with Central Depository and Clearing (CDSC) and trading by brokers.
• Trading has moved to an online system, with demat accounts, mero share, ASBA for IPO applications and T+3 settlement.
• Listed companies are dominated by commercial banks, development banks, finance companies, insurance companies and hydropower firms. Banking is the largest sector by market capitalisation.
• The market has grown a great deal in number of investors and turnover, but it remains small compared with the size of the economy.
• It is volatile and sentiment-driven, affected by interest rates, liquidity in the banking system and margin lending.
• Weaknesses include a shortage of diverse instruments (few derivatives or bond products), speculation, weak information disclosure and low participation of institutional investors.
• Reforms in progress include a secondary regulator, margin trading rules, market makers, and a shift toward a more diversified listing.

Variances: $\sigma_A^2=12^2=144$, $\sigma_B^2=20^2=400$, $Cov_{AB}=72$ (check: $0.30\times12\times20=72$).

(a) Minimum variance portfolio

$w_A=\frac{\sigma_B^2-Cov_{AB}}{\sigma_A^2+\sigma_B^2-2Cov_{AB}}=\frac{400-72}{144+400-144}=\frac{328}{400}=0.82$ $w_B=1-0.82=0.18$

The minimum variance portfolio is 82% in Fund A and 18% in Fund B.

(b) Expected return

$E(R_p)=0.82(8\%)+0.18(13\%)=6.56+2.34=8.90\%$

(c) Standard deviation

$\sigma_p^2=(0.82)^2(144)+(0.18)^2(400)+2(0.82)(0.18)(72)$ $=96.83+12.96+21.25=131.04$ $\sigma_p=\sqrt{131.04}=11.45\%$

(d) Conclusion

• The minimum variance portfolio has a standard deviation (11.45%) lower than that of even the less risky fund, A (12%), while its expected return (8.9%) is higher than A's 8%.
• This is the benefit of diversification: because the correlation (0.30) is well below 1, the risks partly offset.
• A rational investor would not hold 100% of Fund A, because the combination dominates it. Only portfolios above the minimum variance point (more Fund B) are on the efficient frontier, giving higher return in exchange for higher risk.

(a) Index values on 16 July 2021 (base date 16 July 2020)

Market values (shares × price):

(i) Value-weighted $\frac{168{,}000{,}000}{135{,}000{,}000}\times100=124.44$ The total market value of the four stocks rose by 24.44% over the year.

(ii) Price-weighted

Sum of prices: 2020 = 2,300; 2021 = 600 + 2,000 + 300 + 40 = 2,940. $\frac{2{,}940}{2{,}300}\times100=127.83$ (equivalently, average price rises from Rs 575 to Rs 735). The index rose 27.83%, driven largely by high-priced stock B.

(iii) Equally-weighted

Returns: A = $-40\%$, B = $+100\%$, C = $+50\%$, D = $-60\%$. $\text{Average}=\frac{-40+100+50-60}{4}=12.5\%\;\Rightarrow\;\text{Index}=112.5$ Each stock counts equally, so the gain is smaller than in the other two indices.

The three results differ because of weighting: B dominates the price-weighted index through its high price, and both B and A matter most in the value-weighted index through market capitalisation.

(b) Uses of a market index

• A benchmark for evaluating the performance of portfolios and fund managers.
• A measure of overall market movement and investor sentiment.
• An indicator of economic conditions (a barometer of the economy).
• The base for index funds, ETFs and derivatives.
• Used to estimate market return and beta in models such as CAPM.
• Helps in forecasting and technical analysis.

Financial assets are claims on the income or assets of a company, government or other issuer, represented by a contract or document rather than physical form. Their value comes from the cash flows they promise. Examples include shares, bonds, debentures, treasury bills, mutual fund units, bank deposits and derivatives such as futures and options.

Buying on margin means purchasing securities partly with the investor's own money and partly with money borrowed from the broker, with the purchased securities serving as collateral. The investor pays only a percentage of the price (the initial margin). Margin magnifies both gains and losses, and a margin call occurs if equity falls below the maintenance margin.

Short selling is selling a security that the seller does not own, by borrowing it from a broker, with the intention of buying it back later at a lower price and returning it. The profit equals the fall in price (less costs and any dividends owed); the loss is potentially unlimited if the price rises.

Risk is the uncertainty about the future returns of an investment, that is, the possibility that the actual return will differ from the expected return, including the chance of loss. It is commonly measured by the standard deviation or variance of returns, or by beta for systematic risk.

The efficient frontier is the set of portfolios that offer the highest expected return for each level of risk, or the lowest risk for each level of expected return. Plotted with risk (standard deviation) on the x-axis and expected return on the y-axis, it is the upper portion of the curve starting at the minimum variance portfolio. Rational investors choose portfolios only on this frontier.

Yield to call is the yield (internal rate of return) earned by a bondholder if the bond is held until the first call date and redeemed at the call price. It is found by solving $P=\sum_{t=1}^{n}\frac{C}{(1+y)^t}+\frac{\text{Call price}}{(1+y)^n}$ where $n$ is the number of periods to the call date. It is relevant for callable bonds, especially those selling at a premium.

Two leading economic indicators are:

1. Stock market index (such as NEPSE), which tends to rise before an economic recovery.
2. Building permits or new orders for capital goods (also money supply and the yield curve), which signal future activity.

Par value per share: $\frac{\text{Share capital}}{\text{Shares outstanding}}=\frac{1{,}000{,}000}{10{,}000}=\text{Rs }100$

Book value per share:

Total equity $=1{,}000{,}000+500{,}000+1{,}500{,}000=$ Rs 3,000,000 $\frac{3{,}000{,}000}{10{,}000}=\text{Rs }300$

$HPR=\frac{P_1-P_0+D}{P_0}=\frac{250-200+20}{200}=\frac{70}{200}=0.35=35\%$

A zero coupon bond pays no periodic interest, only its face value at maturity, so its value is the present value of the face value discounted at the required yield: $V=\frac{\text{Face value}}{(1+r)^n}$ where $r$ is the required rate of return per period and $n$ is the number of periods to maturity. For example, a Rs 1,000 bond maturing in 5 years at 10% is worth $1{,}000/(1.10)^5=$ Rs 620.92.

An industry passes through stages as it develops, each with a different pattern of sales, profits and risk.

1. Pioneering (start-up) stage: a new product appears. Sales grow rapidly from a small base, but costs are high, profits are small or negative, competition is limited and the risk of failure is very high.
2. Expansion (rapid growth) stage: demand is established and sales and profits grow rapidly. Competitors enter, the product improves and firms need new capital. Risk falls, and the industry is attractive to investors.
3. Maturity (stabilisation) stage: growth slows to about the economy's rate. The market is saturated, competition is intense, margins narrow and only efficient firms survive. Dividends are stable.
4. Decline stage: demand falls because of substitutes, technological change or changing tastes. Sales and profits fall, and firms exit or merge.

Investors use the stage to judge growth, risk and the suitable investment strategy: growth in the early stages, stable income in maturity, and caution in decline.

(a) Total rupee return

Purchase: $400\times150=$ Rs 60,000. Sale: $400\times210=$ Rs 84,000. Dividend: $400\times9=$ Rs 3,600. $\text{Total return}=(84{,}000-60{,}000)+3{,}600=\text{Rs }27{,}600$

(b) Rate of return

$\frac{27{,}600}{60{,}000}=46\%$ (per share: $(210-150+9)/150=69/150=46\%$)

(c) Dividend yield and capital gain

$\text{Dividend yield}=\frac{9}{150}=6\%$ $\text{Capital gain yield}=\frac{210-150}{150}=40\%$

Total: $6\%+40\%=46\%$.

(a) Required return (CAPM)

$k=R_f+\beta(R_m-R_f)=6\%+1.8(14\%-6\%)=6\%+14.4\%=20.4\%$

(b) Pricing

The average (expected) return of 20% is less than the required return of 20.4%. The stock plots slightly below the security market line, so it offers less return than its risk demands. It is slightly overpriced: investors should sell or avoid it, and its price should fall until its expected return rises to 20.4%.

Annual coupon $=8\%\times1{,}000=$ Rs 80. Find $y$ such that $800=\sum_{t=1}^{10}\frac{80}{(1+y)^t}+\frac{1{,}000}{(1+y)^{10}}$

Approximation: $\dfrac{80+(1000-800)/10}{(1000+800)/2}=\dfrac{100}{900}=11.1\%$.

Trial and error:

• At 11%: $80(5.8892)+1000(0.3522)=471.1+352.2=$ Rs 823.3 (too high)
• At 12%: $80(5.6502)+1000(0.3220)=452.0+322.0=$ Rs 774.0 (too low)

Interpolating: $y=11\%+\frac{823.3-800}{823.3-774.0}\times1\%=11\%+0.47\%\approx\mathbf{11.47\%}$

The YTM is about 11.5%, above the coupon rate since the bond sells at a discount.

(a) Required return

$E_1=$ Rs 20, payout 50%, so $D_1=$ Rs 10; plowback $b=0.5$. $g=b\times ROE=0.5\times20\%=10\%$ $P_0=\frac{D_1}{k-g}\;\Rightarrow\;100=\frac{10}{k-0.10}\;\Rightarrow\;k-0.10=0.10\;\Rightarrow\;k=\mathbf{20\%}$

(b) Value compared with no reinvestment

If all earnings were paid out, there would be no growth: $P_0^{NG}=\frac{E_1}{k}=\frac{20}{0.20}=\text{Rs }100$

The difference (the present value of growth opportunities) is $PVGO=100-100=\text{Rs }0$

The value does not exceed it at all, because the reinvestment return (20%) equals the required return (20%). Growth adds no value; the investment projects only earn their cost of capital.

Meaning

An investment is the commitment of money or resources today in the expectation of receiving greater future returns, to compensate for time, inflation and risk. The investment process is the systematic, step-by-step procedure by which an investor decides how to invest funds, from setting goals to monitoring results.

Steps in the investment process

1. Setting investment policy (objectives and constraints): the investor states goals (income, growth, capital preservation), the return expected, the risk tolerance, the investment horizon, liquidity needs, taxes, legal rules and personal circumstances. Wealth and amount available are also determined.
2. Security analysis: securities are examined to find mispriced ones, using
   • Economic, industry and company (fundamental) analysis to estimate intrinsic value,
   • Technical analysis of price and volume trends.
3. Portfolio construction: deciding which securities and how much of each to hold.
   • Asset allocation across stocks, bonds, cash and other assets,
   • Security selection within each class,
   • Diversification and consideration of timing, taxes and transaction costs.
4. Portfolio revision: periodically changing the portfolio by selling poor or overvalued holdings and buying attractive ones as conditions, prices and goals change, weighing the transaction costs.
5. Portfolio performance evaluation: measuring the return and risk of the portfolio and comparing it with a benchmark using measures such as the Sharpe, Treynor and Jensen measures. The results give feedback for revising the policy.

The process is continuous: evaluation leads back to the policy and the cycle repeats.

Industry analysis studies the prospects of an industry as a link between the economy and the individual company. A common approach is:

1. Classify the industry and its place in the economy: determine whether it is cyclical (autos, construction), defensive (food, pharmaceuticals) or growth, and how sensitive it is to the business cycle, interest rates and policy.
2. Identify the stage of the industry life cycle: pioneering, expansion, maturity or decline, which determines growth, profit and risk.
3. Analyse industry structure and competition (Porter's five forces): rivalry among existing firms, threat of new entrants, threat of substitutes, bargaining power of buyers and of suppliers. Concentration, entry barriers and pricing power are also examined.
4. Examine demand and supply: market size, growth rate, demand drivers, capacity and cost structure, and the supply of inputs and raw materials.
5. Study government policy and regulation: taxes, tariffs, licensing, subsidies, environmental and labour laws.
6. Assess technology and other external factors: innovation, changes in consumer tastes, demography, and globalisation.
7. Financial and valuation analysis: industry sales, profit margins, ROE, earnings growth, and industry P/E compared with its history and with other industries.
8. Forecast industry earnings and conclude: forecast sales, earnings and dividends, judge whether the industry is attractive, and select the best firms in the industry for investment.

The result is used to overweight attractive industries and avoid weak ones in the portfolio.

Cost of 100 shares at Rs 500 = Rs 50,000.

(a) Initial margin 75%

• Own money invested $=0.75\times50{,}000=$ Rs 37,500
• Borrowed from broker $=$ Rs 12,500
• Interest at 8%: Rs 1,000

(b) Rate of return (loan plus interest repaid = Rs 13,500)

(c) Initial margin 50%

• Own money $=$ Rs 25,000; borrowed $=$ Rs 25,000; interest $=$ Rs 2,000, so repayment is Rs 27,000.

Effect of margin: without borrowing, the returns would be $-20\%$, $0\%$, $+20\%$. Margin buying leverages the position: the lower the initial margin, the larger the gain when the price rises (+24% at 75% margin, +32% at 50% margin) and the larger the loss when it falls (-29.3% and -48%). Interest cost also reduces returns, so margin increases both return and risk, and brings the possibility of margin calls.

(a) Price-weighted index

Index $=\dfrac{\sum P}{\text{number of stocks}}$

• Day 1: $(400+200+1{,}600)/3=2{,}200/3=733.33$
• Day 2: $(500+220+1{,}600)/3=2{,}320/3=773.33$
• Day 3: $(600+240+1{,}800)/3=2{,}640/3=880.00$

Percentage change: $\text{Day 2}=\frac{773.33-733.33}{733.33}=5.45\%,\qquad \text{Day 3}=\frac{880-773.33}{773.33}=13.79\%$

(b) Value-weighted index

Market values:

• Day 1 = 100
• Day 2 $=\dfrac{8{,}060{,}000}{7{,}800{,}000}\times100=103.33$
• Day 3 $=\dfrac{9{,}120{,}000}{7{,}800{,}000}\times100=116.92$

Percentage change: $\text{Day 2}=3.33\%,\qquad \text{Day 3}=\frac{116.92-103.33}{103.33}=13.15\%$

(c) Adjusting for a stock split

Price-weighted index: a split lowers the price and would artificially reduce the index, so the divisor is adjusted to keep the index unchanged. Example: on day 3, stock C splits 2-for-1, so its price becomes Rs 900. The sum of prices becomes $600+240+900=1{,}740$. The new divisor is $d=\frac{1{,}740}{880}=1.977$ The index stays at 880. On the next day, the index is the new sum of prices divided by 1.977.

Value-weighted index: no adjustment is needed, because the split halves the price but doubles the number of shares, so market value is unchanged. In the example, C's value stays at $8{,}000\times900=$ Rs 7,200,000 and the index remains 116.92. Only new issues, buybacks or delistings require changing the base market value.

(a) Weights: $w_A = 9/10 = 0.9$, $w_B = 1/10 = 0.1$.

Expected return:

$E(R_p) = 0.9(10\%) + 0.1(15\%) = 10.5\%$

Risk (with $\rho_{AB} = -0.50$):

$\sigma_p^2 = w_A^2\sigma_A^2 + w_B^2\sigma_B^2 + 2w_Aw_B\rho\sigma_A\sigma_B$

$\sigma_p^2 = (0.81)(25) + (0.01)(100) + 2(0.9)(0.1)(-0.5)(5)(10) = 20.25 + 1 - 4.5 = 16.75$

$\sigma_p = \sqrt{16.75} = 4.09\%$

The portfolio risk (4.09%) is lower than that of Stock A (5%) and Stock B (10%). So the portfolio is less risky than either investment alone, because of the negative correlation (diversification).

(b) The minimum-variance proportion is:

$w_A = \frac{\sigma_B^2 - \rho\sigma_A\sigma_B}{\sigma_A^2 + \sigma_B^2 - 2\rho\sigma_A\sigma_B} = \frac{100 + 25}{25 + 100 + 50} = \frac{125}{175} = 0.7143$

$w_B = 1 - 0.7143 = 0.2857$

Investment: Stock A = $0.7143 \times 10 =$ Rs 7.143 million; Stock B = $0.2857 \times 10 =$ Rs 2.857 million.

$E(R_p) = 0.7143(10) + 0.2857(15) = 11.43\%$

$\sigma_p^2 = (0.5102)(25) + (0.0816)(100) + 2(0.7143)(0.2857)(-0.5)(50) = 12.755 + 8.163 - 10.204 = 10.714$

$\sigma_p = 3.27\%$

(c) Rs 5 million goes into government securities (weight 0.5, return 5%, risk 0) and Rs 5 million into the portfolio of part (a) (weight 0.5, return 10.5%, risk 4.09%).

$E(R) = 0.5(5\%) + 0.5(10.5\%) = 7.75\%$

$\sigma = 0.5 \times 4.09\% = 2.05\%$

(d) The optimal risky portfolio is the one with the highest reward-to-variability (Sharpe) ratio, using $r_f = 5\%$. Excess returns: $A = 10 - 5 = 5$, $B = 15 - 5 = 10$.

$w_A = \frac{(5)(100) - (10)(-0.5)(5)(10)}{(5)(100) + (10)(25) - (5+10)(-0.5)(5)(10)} = \frac{500 + 250}{500 + 250 + 375} = \frac{750}{1125} = 0.6667$

$w_B = 0.3333$

$E(R_{opt}) = 0.6667(10) + 0.3333(15) = 11.67\%$

$\sigma^2 = (0.4444)(25) + (0.1111)(100) + 2(0.6667)(0.3333)(-0.5)(50) = 11.11 + 11.11 - 11.11 = 11.11$

$\sigma_{opt} = 3.33\%$

Sharpe ratio $= (11.67 - 5)/3.33 = 2.0$, the highest possible. On Rs 10 million this means about Rs 6.67 million in Stock A and Rs 3.33 million in Stock B. Ramhari then mixes this risky portfolio with government securities according to his risk tolerance. For example, with 50% in government securities the complete portfolio earns $0.5(5) + 0.5(11.67) = 8.33\%$ with risk $0.5(3.33) = 1.67\%$. This is better than the 7.75% return at 2.05% risk in part (c).

Investment is the commitment of money or other resources today with the expectation of earning a greater return in the future. It involves sacrificing present consumption for future benefit, and the return compensates for time, expected inflation and risk.

Real assets (land, buildings, machinery, knowledge) are physical or productive assets that directly create goods and services and generate income for the economy. Financial assets (shares, bonds, deposits) are claims on the income generated by real assets; they only distribute income or wealth among investors and do not by themselves create it.

A value-weighted index (market-capitalisation weighted index) is a stock index in which each stock's weight is proportional to its total market value (price × number of shares outstanding). Larger companies therefore influence the index more than smaller ones. The NEPSE index and the S&P 500 are examples.

$\text{Index} = \frac{\sum P_t Q_t}{\sum P_0 Q_0}\times \text{base value}$

The primary market is the market where new securities are issued for the first time by companies or the government to raise fresh capital directly from investors, for example through an IPO, FPO, rights issue or bond issue. The money goes to the issuer.

Any three assumptions of CAPM:

1. Investors are rational, risk-averse and choose portfolios on the basis of mean return and variance (Markowitz efficient portfolios).
2. All investors have homogeneous expectations and the same single-period investment horizon.
3. Investors can borrow and lend unlimited amounts at the same risk-free rate, and the market is perfect (no taxes, no transaction costs, assets are perfectly divisible).

Fiscal policy is the government's use of taxation, public spending and borrowing to influence the level of economic activity, employment, inflation and growth. Increasing spending or cutting taxes is expansionary; reducing spending or raising taxes is contractionary.

Two lagging economic indicators are:

1. Unemployment rate (duration of unemployment).
2. Consumer price index (inflation) or the average prime/bank lending rate.

They change after the economy has already begun to follow a new trend, and so confirm it.

The dividend is a perpetuity, so

$P_0 = \frac{D}{k} = \frac{20}{0.10} = \text{Rs } 200$

The present value of the stock is Rs 200 per share.

With an initial margin of 50%, the equity Rabi puts in is half of the purchase value.

$\text{Maximum purchase} = \frac{500{,}000}{0.50} = \text{Rs } 1{,}000{,}000$

Rabi can buy stock worth Rs 1,000,000 by borrowing Rs 500,000 from the broker.

Holding period yield:

$\text{Yield} = \frac{P_1 - P_0 + D}{P_0} = \frac{180 - 200 + 10}{200} = \frac{-10}{200} = -5\%$

Mahesh earned a return of −5% (a loss of Rs 1,000 on 100 shares, which is Rs 10 per share).

The financial system brings together those who have surplus funds and those who need funds. Its main players are:

• Households (individuals): net savers who supply funds by investing in deposits, shares and bonds.
• Business firms: mainly net borrowers who raise funds by issuing shares and bonds or by taking loans to finance projects.
• Government: raises funds by issuing treasury bills and bonds, and regulates the system; it also invests surplus funds.
• Financial intermediaries: commercial banks, development banks, insurance companies, mutual funds, pension funds and cooperatives collect small savings and lend or invest them, reducing cost and risk.
• Financial markets: the money market and capital market (primary and secondary), such as NEPSE, where securities are issued and traded.
• Regulators and supporting institutions: Nepal Rastra Bank, SEBON, Insurance Authority, brokers, merchant bankers, and credit rating agencies, which supervise and facilitate the system.
• Foreign investors and institutions: supply external funds and add liquidity.

The domestic macro economy is affected by the following factors.

1. Fiscal policy: government spending, taxation and public borrowing affect demand, income and employment.
2. Monetary policy: the central bank's control of money supply, interest rates, CRR and SLR influences credit, investment, inflation and exchange rates.
3. Inflation: rising prices reduce purchasing power and raise interest rates and the cost of production.
4. Interest rates: high rates discourage investment and consumption, low rates encourage them.
5. Exchange rate and balance of payments: remittance, exports and imports, and foreign reserves affect the economy, especially in a remittance-dependent country like Nepal.
6. Savings, investment and capital formation: these decide the economic growth.
7. Business cycle, employment and demand: booms and recessions change output and income.
8. Political stability and legal environment: stability and sound regulation improve confidence and investment.
9. Natural, social and global factors: monsoon, disasters, population and global prices or recessions (such as oil prices and COVID-19).

(a) The market portfolio has a beta of 1, so its expected return is 12%.

(b) A stock with zero beta has no systematic risk, so it earns the risk-free rate of 4%.

(c) Required return by CAPM:

$E(R) = 4\% + 0.5\,(12\% - 4\%) = 8\%$

Expected return from the investment:

$\frac{3 + 41}{40} - 1 = 10\%$

The expected return (10%) is greater than the required return (8%), i.e. alpha = +2%. The stock is underpriced. Its fair price is 44/1.08 = Rs 40.74, which is above the market price of Rs 40.

(a) Weights: 50% risky portfolio, 50% risk-free.

$E(R_p) = 0.5(15\%) + 0.5(7\%) = 11\%$

$\sigma_p = 0.5 \times 22\% = 11\%$

(b) Slope of the CAL (reward-to-variability ratio):

$\frac{E(R_P)-R_f}{\sigma_P} = \frac{15-7}{22} = 0.3636$

(c) Total invested in the risky asset = 300,000 + 120,000 = Rs 420,000, so the weight in the risky portfolio is $y = 420{,}000/300{,}000 = 1.4$ and the weight in the risk-free asset is −0.4.

$E(R_p) = 7\% + 1.4(15\% - 7\%) = 18.2\%$

$\sigma_p = 1.4 \times 22\% = 30.8\%$

The slope of the CAL is $(18.2-7)/30.8 = 0.3636$, the same as before. Because the investor borrows at the same risk-free rate, the leveraged portfolio stays on the same straight line; it moves further up the CAL, taking more risk for proportionately more return, but the reward-to-variability ratio does not change.

(a) Holding period return (HPR) = (Ending value − Beginning value + Cash flow) / Beginning value.

$HPR_{ABC}=\frac{130{,}000-120{,}000+15{,}000}{120{,}000}=\frac{25{,}000}{120{,}000}=20.83\%$

$HPR_{XYZ}=\frac{185{,}000-155{,}000+16{,}800}{155{,}000}=\frac{46{,}800}{155{,}000}=30.19\%$

(b) Since the two investments are equally risky, Mr. Pandey should recommend XYZ. For the same level of risk, a rational investor prefers the higher return, and XYZ's 30.19% is well above ABC's 20.83%.

Short sale: 100 shares at Rs 300 = Rs 30,000 value of the short position.

(a) Proceeds from the short sale provided by the broker = $100\times 300 =$ Rs 30,000 (held by the broker as collateral).

(b) Initial margin of 50% must be deposited in cash:

$0.50\times 30{,}000 = \text{Rs } 15{,}000$

Total collateral in the account = 30,000 + 15,000 = Rs 45,000.

(c) Margin call occurs when equity / value of shares owed falls to the 30% maintenance margin. Equity $=45{,}000-100P$.

$\frac{45{,}000-100P}{100P}=0.30\;\Rightarrow\;45{,}000=130P\;\Rightarrow\;P=\text{Rs } 346.15$

A margin call is received when the price rises to about Rs 346.15.

(d) At P = Rs 400: value of shares owed = Rs 40,000; equity = 45,000 − 40,000 = Rs 5,000. Required equity = 0.30 × 40,000 = Rs 12,000.

$\text{Deposit needed}=12{,}000-5{,}000=\text{Rs } 7{,}000$

Investment process is the systematic, step-by-step procedure by which an investor decides how much to invest, in which assets, and how to manage and review the portfolio so as to achieve his or her financial goals. It links the investor's objectives and constraints with the choice of securities and the continuing control of the portfolio.

Steps in the investment process

1. Setting investment policy. The investor states objectives (income, growth, capital preservation), return and risk requirements, and constraints such as investable wealth, time horizon, liquidity needs, tax position, legal restrictions and personal preferences. The policy also fixes the target asset mix (e.g. stocks, bonds, cash) and the investor's risk tolerance.

2. Security analysis. The available securities and markets are examined to find mispriced assets. This includes

   • Fundamental analysis: economy, industry and company analysis to estimate intrinsic value (using dividends, earnings, P/E, etc.).
   • Technical analysis: study of past price and volume patterns to predict future movement.

3. Portfolio construction. Identify the specific assets to hold and the proportion of wealth in each. Issues are asset allocation, security selection, and timing, with diversification used to reduce risk for a given return, in line with the policy set in step 1.

4. Portfolio revision. As the investor's circumstances, market conditions and security prices change, the portfolio is rebalanced by selling some securities and buying others, weighed against transaction costs and taxes.

5. Portfolio performance evaluation. Actual return and risk are measured and compared against a benchmark (e.g. NEPSE index) using measures such as Sharpe, Treynor and Jensen indices. The findings feed back into the investment policy and the process repeats.

Thus the investment process is a continuous cycle: policy, analysis, construction, revision and evaluation.

(a) Price-weighted index

Day 1: sum of prices = 350 + 450 + 1,200 = 2,000

$\text{Index}_1=\frac{2{,}000}{2.5}=800$

Day 2: sum of prices = 375 + 440 + 1,225 = 2,040. No split or change in constituents, so the divisor stays 2.5.

$\text{Index}_2=\frac{2{,}040}{2.5}=816$

$\text{Change}=\frac{816-800}{800}=2.0\%$

(b) Value-weighted index (market capitalisation, shares in thousands)

Taking Day 1 as base = 100, Day 2 index = (1,647,500 / 1,625,000) × 100 = 101.38.

$\text{Change}=\frac{1{,}647{,}500-1{,}625{,}000}{1{,}625{,}000}=1.38\%$

(c) Why the changes differ. The price-weighted index gives weight to the absolute share price, so high-priced stock C (and A's Rs 25 rise) dominate, whereas the value-weighted index weights each stock by total market capitalisation. Stock B has the largest capitalisation in the value-weighted index (about 41% on Day 1), and its price fell, which pulls the value-weighted change down to 1.38% against 2.0%.

(d) Limitation of a price-weighted index. It ignores company size: a high-priced stock with small market value has more influence than a low-priced large company. Also, stock splits and stock dividends reduce a share's price and so alter its weight, which forces the divisor to be adjusted, and the index does not reflect true market value movements.

(a) Ram (dividend growth model)

$D_1=D_0(1+g)=10(1.08)=\text{Rs }10.80$

$V=\frac{D_1}{k-g}=\frac{10.80}{0.15-0.08}=\frac{10.80}{0.07}=\text{Rs }154.29$

Strategy: if the market price is below Rs 154.29 the stock is undervalued, so buy; if above, it is overvalued, so sell (or avoid); if equal, hold.

(b) Laxman (P/E approach)

$V=\text{P/E}\times EPS=20\times 30=\text{Rs }600$

Strategy: buy if the market price is below Rs 600 (undervalued), sell if above Rs 600 (overvalued), hold if equal.

(c) Bharat (book value approach)

Total equity = paid-in capital 50,000,000 + retained earnings 50,000,000 = Rs 100,000,000.

$\text{Book value per share}=\frac{100{,}000{,}000}{1{,}000{,}000}=\text{Rs }100$

Strategy: buy if the market price is below Rs 100, sell if it is well above book value.

(d) Final price. Taking the average of the three estimates:

$\frac{154.29+600+100}{3}=\frac{854.29}{3}\approx\text{Rs }284.76$

(e) Final strategy at market price Rs 600. The market price of Rs 600 is much higher than the final estimated value of Rs 284.76 (more than double), so the stock is overvalued. The investor should sell the shares if held (or not buy), and wait for the price to fall near the intrinsic value.

Given: coupon = 11% × 1,000 = Rs 110 per year, n = 15, price $P_0$ = Rs 900, par = Rs 1,000.

(a) Yield to maturity. YTM is the rate $y$ satisfying

$900=\sum_{t=1}^{15}\frac{110}{(1+y)^t}+\frac{1{,}000}{(1+y)^{15}}$

Approximation: $\dfrac{110+(1000-900)/15}{(1000+900)/2}=\dfrac{116.67}{950}=12.28\%$.

Trial and error refines this: at 12% the value is about Rs 931.9 (too high); at 13% it is about Rs 873.4 (too low). Interpolating gives

$\text{YTM}\approx 12.5\%$

(b) Current yield

$CY=\frac{\text{Annual coupon}}{\text{Market price}}=\frac{110}{900}=12.22\%$

(c) Value if YTM falls to 10%

$V=110\times PVIFA_{10\%,15}+1{,}000\times PVIF_{10\%,15}=110(7.6061)+1{,}000(0.2394)$

$V=836.67+239.39\approx\text{Rs }1{,}076.06$

(d) Effect of YTM on bond value. Bond value and yield move in opposite directions. When required yield (YTM) rises above the coupon rate, the bond sells at a discount (as at Rs 900 here); when it falls, the bond price rises and sells at a premium (Rs 1,076 at 10%). Price changes are larger for longer maturities and lower coupons.

Data: Stock fund S: $E(r)=15\%$, $\sigma=32\%$. Bond fund B: $E(r)=9\%$, $\sigma=23\%$. $\rho=0.15$, $r_f=5.5\%$.

Covariance $=0.15\times0.32\times0.23=0.01104$.

(a) Opportunity set. For weight $w$ in the stock fund:

$E(r_p)=15w+9(1-w),\qquad \sigma_p=\sqrt{w^2(0.32)^2+(1-w)^2(0.23)^2+2w(1-w)(0.01104)}$

Plotting these points with standard deviation on the x-axis and expected return on the y-axis gives a curve bending to the left, with its leftmost point near $w\approx 30\%$ in stocks.

Minimum variance portfolio:

$w_S=\frac{\sigma_B^2-Cov}{\sigma_S^2+\sigma_B^2-2Cov}=\frac{0.0529-0.01104}{0.1024+0.0529-0.02208}=\frac{0.04186}{0.13322}=0.3142$

So 31.42% stocks and 68.58% bonds, with expected return about 10.89% and standard deviation about 19.94%.

(b) Optimal risky portfolio (tangent from $r_f=5.5\%$). Excess returns: stocks 9.5%, bonds 3.5%.

$w_S=\frac{9.5(0.0529)-3.5(0.01104)}{9.5(0.0529)+3.5(0.1024)-(9.5+3.5)(0.01104)}=\frac{0.50255-0.03864}{0.50255+0.3584-0.14352}=\frac{0.46391}{0.71743}=0.6466$

So the optimal risky portfolio has 64.66% in the stock fund and 35.34% in the bond fund, with

$E(r_P)=0.6466(15)+0.3534(9)=12.88\%,\qquad \sigma_P\approx 23.34\%$

The tangent line from 5.5% touches the opportunity set at about this point.

(c) Reward-to-variability ratio of the best CAL

$S=\frac{E(r_P)-r_f}{\sigma_P}=\frac{12.88-5.5}{23.34}=0.316$

(d) Required expected return of 12% on the CAL

(i) Let $y$ be the fraction in the optimal risky portfolio:

$12=5.5+y(12.88-5.5)\Rightarrow y=\frac{6.5}{7.38}=0.8808$

$\sigma=y\sigma_P=0.8808\times23.34\approx 20.56\%$

(ii) Proportions:

• T-bill fund: $1-0.8808=$ 11.92%
• Stock fund: $0.8808\times0.6466=$ 56.95%
• Bond fund: $0.8808\times0.3534=$ 31.12%

(Check: 56.95 + 31.12 + 11.92 = 99.99, i.e. 100% allowing for rounding.)