Security Market Line - Finance

1. Given the information in the passage, what is the position of the combined portfolio relative to the Security Market Line (SML)?
   Answer: The portfolio plots below the SML. First, calculate the portfolio's beta: β_p = $w_A$ × β_A + $w_B$ × β_B = 0.60(1.2) + 0.40(0.9) = 0.72 + 0.36 = 1.08. Second, calculate the portfolio's expected return: E($R_p$) = $w_A$ × E($R_A$) + $w_B$ × E($R_B$) = 0.60(13%) + 0.40(9%) = 7.8% + 3.6% = 11.4%. Third, calculate the portfolio's required return using the SML: R_required = $R_f$ + β_p × [E($R_M$) - $R_f$] = 3% + 1.08 × (11% - 3%) = 3% + 1.08 × 8% = 3% + 8.64% = 11.64%. Since the portfolio's expected return (11.4%) is less than its required return (11.64%), it plots below the SML and is overvalued.
2. A large manufacturing firm, currently with a beta of 1.1, announces a major acquisition of a regulated utility company. Regulated utilities are known for stable earnings and low systematic risk. Assuming the market views this acquisition as a significant de-risking event for the firm, what is the most likely immediate impact on the firm's stock relative to the SML?
   Answer: The stock's position will move down and to the left along the SML. The acquisition of a low-risk utility company will lower the overall systematic risk of the combined firm. This means the firm's beta will decrease from 1.1. According to the SML, a lower beta corresponds to a lower required return. Therefore, the stock's equilibrium position will move to a new point on the SML that is to the left (lower beta) and down (lower required return). This represents a movement along the SML, not a shift of the SML itself or an immediate mispricing.
3. Assume the central bank takes unexpected actions that cause the risk-free rate to rise. Simultaneously, increased geopolitical tensions lead investors to demand a higher premium for bearing market risk. How will these two events affect the Security Market Line (SML)?
   Answer: The SML will shift up and become steeper. The SML is defined by the equation E($R_i$) = $R_f$ + β_i * [E($R_M$) - $R_f$]. The intercept of the SML is the risk-free rate ($R_f$). An increase in the risk-free rate will cause a parallel upward shift in the entire line. The slope of the SML is the market risk premium [E($R_M$) - $R_f$]. When investors demand a higher premium for bearing market risk (i.e., they become more risk-averse), the slope increases, making the SML steeper. Therefore, the combination of these events causes the SML to shift up and become steeper.
4. An analyst determines that Stock XYZ is fairly priced in the market. The stock has a beta of 1.5 and an expected annual return of 14%. If the current T-bill rate is 5%, what is the implied expected return on the market?
   Answer: 11.0% If a stock is fairly priced, its expected return must equal its required return as per the SML. The SML equation is E($R_i$) = $R_f$ + β_i * [E($R_M$) - $R_f$]. We are given E(R_XYZ) = 14%, $R_f$ = 5%, and β_XYZ = 1.5. Plugging these values in: 14% = 5% + 1.5 * [E($R_M$) - 5%]. Solving for the market risk premium [E($R_M$) - 5%]: 9% = 1.5 * [E($R_M$) - 5%], so [E($R_M$) - 5%] = 9% / 1.5 = 6%. This 6% is the market risk premium. The question asks for the expected return on the market, E($R_M$), which is E($R_M$) = $R_f$ + Market Risk Premium = 5% + 6% = 11.0%.
5. A stock is currently trading at $80 per share. Analysts forecast that the stock's price will be $85 in one year, with no dividends paid. The stock has a beta of 1.3, the risk-free rate is 3%, and the market risk premium is 6%. Based on an analysis using the Security Market Line (SML), the stock is most likely:
   Answer: Overvalued, because its required return is 10.8% and its expected return is 6.25%. This is a multi-step problem. First, calculate the stock's expected return: E(R) = (P1 - P0) / P0 = ($85 - $80) / $80 = $5 / $80 = 6.25%. Second, calculate the stock's required return using the SML (CAPM) formula: R_required = $R_f$ + β (Market Risk Premium) = 3% + 1.3 (6%) = 3% + 7.8% = 10.8%. Since the expected return (6.25%) is less than the required return (10.8%), the stock is considered overvalued. Its price is too high for the return it is expected to generate, given its level of systematic risk.
6. A U.S.-based analyst is evaluating a company located entirely within a developing nation. The analyst determines the following: U.S. T-bill rate = 2%, global equity market risk premium = 5.5%, stock's beta relative to the global index = 1.4, and an estimated country risk premium for the nation = 3.5%. Using the CAPM modified for country risk, what is the estimated required rate of return for this stock?
   Answer: 13.2% A common method for adjusting the CAPM for country risk is to add the country risk premium (CRP) to the standard CAPM formula. The formula is: R_required = $R_f$ + β (Market Risk Premium) + CRP. Plugging in the values: R_required = 2% + 1.4 (5.5%) + 3.5% = 2% + 7.7% + 3.5% = 13.2%. Distractors may result from omitting the CRP (9.7%), incorrectly adding the CRP into the market premium before multiplying by beta (2% + 1.4 * (5.5% + 3.5%) = 14.6%), or omitting beta (2% + 5.5% + 3.5% = 11.0%).
7. An analyst observes that in a particular market, a large number of securities are currently plotting below the Security Market Line. Assuming the CAPM is the correct asset pricing model, what is the most likely implication of this observation?
   Answer: Market forces will likely drive the prices of these securities down, increasing their future expected returns. Securities that plot below the SML are overvalued. Their expected returns are insufficient to compensate for their level of systematic risk (beta). In an efficient market, this situation would create selling pressure on these securities. As investors sell, the prices of these securities will fall. A lower price, holding future cash flows constant, implies a higher future expected return. This process continues until the securities' expected returns rise to the level of the SML, bringing the market back to equilibrium.
8. An analyst is reviewing two stocks, Stock A and Stock B. Both stocks have a required return of 12% according to the SML. Stock A has an expected return of 14% and a standard deviation of 40%. Stock B has an expected return of 13% and a standard deviation of 25%. According to the SML framework, which of the following actions is most appropriate?
   Answer: Prefer Stock A because it has a higher positive alpha. When you encounter questions about the Security Market Line (SML), focus on the concept of alpha—the difference between a stock's expected return and its required return based on systematic risk. The SML framework tells us whether securities are undervalued, overvalued, or fairly valued relative to their risk. To find each stock's alpha, subtract the required return from the expected return. Stock A's alpha is $14\% - 12\% = +2\%$, while Stock B's alpha is $13\% - 12\% = +1\%$. A positive alpha indicates the stock is expected to outperform what the SML predicts, making it undervalued and attractive to investors. Answer D is correct because Stock A has the higher positive alpha (+2% vs +1%), suggesting it offers better risk-adjusted returns than what the market requires. This makes it the preferred investment under SML analysis. Answer A is wrong because it focuses on total risk (standard deviation) rather than systematic risk. The SML only considers systematic risk—total risk includes unsystematic risk that can be diversified away, so it's irrelevant for pricing decisions. Answer B incorrectly suggests rejecting stocks based on high standard deviations. The SML framework doesn't set absolute limits on volatility; it only cares whether expected returns adequately compensate for systematic risk. Answer C misunderstands the analysis. Having the same required return doesn't mean indifference—you should prefer the stock with higher expected return relative to that requirement. Remember: In SML questions, always calculate alpha first. The stock with the highest positive alpha is typically the best choice, regardless of total risk measures.
9. Stock K has an expected return of 12%. The risk-free rate is 4% and the market risk premium is 5%. If the stock is currently undervalued and has an alpha of +1.5%, what is the implied beta of Stock K?
   Answer: 1.3 This is a multi-step problem that requires working backwards. First, use the definition of alpha: Alpha = E(R_actual) - R_required. We are given Alpha = +1.5% and E(R_actual) = 12%. So, 1.5% = 12% - R_required. Solving for the required return gives R_required = 12% - 1.5% = 10.5%. Second, use the SML equation to find beta: R_required = $R_f$ + β (Market Risk Premium). Plugging in the values: 10.5% = 4% + β (5%). Solving for β: 6.5% = β * (5%), so β = 6.5% / 5% = 1.3. A common trap is to use the 12% expected return directly in the SML equation, which would incorrectly yield a beta of 1.6.
10. If the assumption of frictionless markets (no transaction costs or taxes) in the CAPM were violated, what would be the most likely observable effect on securities in relation to the Security Market Line?
    Answer: Securities might plot within a band around the SML, as minor mispricings may not be large enough to be profitably arbitraged. The SML describes an equilibrium relationship where all assets are priced perfectly. This relies on arbitrage to correct any mispricings. In the real world, transaction costs and taxes create a barrier to arbitrage. A security might be slightly mispriced (e.g., plot slightly above or below the SML), but if the potential profit from trading on this mispricing is less than the transaction costs involved, no arbitrage will occur. This would result in securities plotting within a 'band' or 'range' around the SML, rather than perfectly on it.
11. The SML for the current market is defined by the equation: E(R) = 0.04 + 0.07β. An analyst determines that Stock Q has a Jensen's alpha of +2.5% and a beta of 1.2. What is the total expected return for Stock Q?
    Answer: 14.9% This is a multi-step problem. First, use the SML equation to find the required return for Stock Q based on its beta. R_required = 0.04 + 0.07 * (1.2) = 0.04 + 0.084 = 0.124 or 12.4%. Second, use the definition of Jensen's alpha, which is the difference between the stock's actual expected return and its required return: Alpha = E(R_actual) - R_required. We can rearrange this to find the expected return: E(R_actual) = R_required + Alpha. Plugging in the values: E(R_actual) = 12.4% + 2.5% = 14.9%.
12. A security has a beta of -0.4. The risk-free rate is 2%, and the expected market return is 8%. According to the Capital Asset Pricing Model, which statement about this security is most accurate?
    Answer: The security's required return is less than the risk-free rate, and it could be valuable for portfolio diversification. The required return is calculated using the SML: R_required = $R_f$ + β * [E($R_M$) - $R_f$] = 2% + (-0.4) (8% - 2%) = 2% - 0.4 (6%) = 2% - 2.4% = -0.4%. This required return is less than the risk-free rate. A negative beta security moves counter-cyclically to the market, providing significant diversification benefits by reducing overall portfolio variance. Therefore, despite its low (or even negative) required return, it can be a valuable addition to a well-diversified portfolio.
13. A zero-beta portfolio has been constructed by an asset manager. If the Capital Asset Pricing Model holds, what should the expected return of this portfolio be, and why?
    Answer: Equal to the risk-free rate, as the SML shows this is the required return for a beta of zero. The Security Market Line equation is E($R_i$) = $R_f$ + β_i * [E($R_M$) - $R_f$]. For a zero-beta portfolio, β_i = 0. Substituting this into the equation gives E($R_i$) = $R_f$ + 0 * [E($R_M$) - $R_f$] = $R_f$. Therefore, according to the CAPM, any asset or portfolio with zero systematic risk must have an expected return equal to the risk-free rate. This is the intercept of the SML. Unsystematic risk is irrelevant because it is not priced by the market.
14. An investor holds a portfolio that lies on the Security Market Line with a beta of 0.8. The risk-free rate is 3% and the market risk premium is 7.5%. The investor then sells a portion of the portfolio and buys shares of Stock Y. The new, combined portfolio now has a beta of 0.9, but its expected return is lower than the original portfolio's expected return. This implies that Stock Y:
    Answer: is overvalued and plots below the SML. This question tests your understanding of the Security Market Line (SML) and how portfolio changes affect expected returns. When you see a scenario where adding a stock to a portfolio increases beta but decreases expected return, immediately think about whether that stock is properly priced according to the Capital Asset Pricing Model. Let's work through the math. The original portfolio has a beta of 0.8 and lies on the SML, so its expected return is: $E(R) = 3\% + 0.8 \times 7.5\% = 9\%$. After adding Stock Y, the new portfolio has a beta of 0.9. If Stock Y were fairly priced (on the SML), the new portfolio's expected return should be: $E(R) = 3\% + 0.9 \times 7.5\% = 9.75\%$. However, the problem states the new portfolio's expected return is lower than 9%. This means Stock Y must be offering insufficient return for its level of risk—it's overvalued and plots below the SML. Choice A is wrong because if Stock Y had a beta lower than 0.8, adding it couldn't increase the portfolio beta to 0.9. Choice B is incorrect because zero alpha means the stock lies exactly on the SML, which would increase the portfolio's expected return, not decrease it. Choice C is backwards—an undervalued stock above the SML would increase the portfolio's expected return. Remember this pattern: when adding a stock increases portfolio beta but decreases expected return, that stock is always overvalued and plots below the SML. The stock isn't providing adequate compensation for its systematic risk.
15. An analyst is explaining the distinction between the Security Market Line (SML) and the Capital Market Line (CML). A key difference is the measure of risk used on the horizontal axis.
    Answer: The SML uses beta, which measures only non-diversifiable risk, making it applicable to any individual security or portfolio. The SML plots the relationship between required return and systematic risk. The correct measure for systematic risk is beta (β). Beta measures how an asset's return moves in relation to the overall market and represents risk that cannot be diversified away. Because the SML focuses on the risk that is priced by the market, it uses beta and is applicable to any asset, whether it's an individual security or a portfolio. In contrast, the CML uses total risk (standard deviation) on its horizontal axis and is only applicable to efficient portfolios.
16. An analyst correctly calculates that according to the SML, the required return on a specific stock is 10%. The analyst also believes the stock has a 50% chance of returning 20% and a 50% chance of returning -5% over the next year. How should the analyst interpret the stock's current valuation?
    Answer: The stock is overvalued because its expected return is less than its required return. This is a two-step problem. First, calculate the probability-weighted expected return of the stock: E(R) = (0.50 20%) + (0.50 -5%) = 10% - 2.5% = 7.5%. Second, compare this expected return to the required return from the SML, which is given as 10%. Since the stock's expected return of 7.5% is less than the required return of 10% for its level of systematic risk, the stock is overvalued.
17. A stock currently trades at $40. It is expected to pay a $1.20 dividend next year, and analysts expect the dividend to grow at a constant 6% annually. The risk-free rate is 3%, the market risk premium is 7%, and the stock's beta is 1.5. According to a joint analysis using the SML and the dividend discount model, the stock is:
    Answer: Overvalued, as its expected return of 9.0% is less than its required return of 13.5%. This requires two calculations. First, find the expected return using the dividend discount model (Gordon Growth Model): E(R) = (D1 / P0) + g = ($1.20 / $40) + 6% = 3% + 6% = 9.0%. Second, find the required return using the SML: R_required = $R_f$ + β (Market Risk Premium) = 3% + 1.5 (7%) = 3% + 10.5% = 13.5%. Since the stock's expected return (9.0%) is significantly lower than its required return (13.5%) for its level of risk, the stock is overvalued.
18. An analyst observes that during a recent economic downturn, investor risk aversion increased substantially. Holding other factors like the risk-free rate and expected market returns constant for a moment, what is the primary consequence of increased risk aversion on the Security Market Line?
    Answer: The slope of the SML increases. The slope of the Security Market Line represents the market risk premium [E($R_M$) - $R_f$]. This premium is the compensation investors demand for taking on one unit of market risk. When investor risk aversion increases, they demand more compensation for the same amount of risk. This directly increases the market risk premium, which in turn increases the slope of the SML, making it steeper. The intercept, which is the risk-free rate, is not directly affected by changes in risk aversion.
19. What is the primary rationale for an investor to short-sell a stock that is observed to be plotting significantly below the Security Market Line?
    Answer: The stock is overvalued, and its price is expected to decrease as its return adjusts upward toward the SML. When you encounter questions about the Security Market Line (SML), focus on the relationship between expected return and systematic risk. The SML represents the required return for any given level of beta - it's what investors should expect to earn based on a stock's systematic risk. A stock plotting significantly below the SML means its expected return is lower than what the model suggests it should be given its risk level. This indicates the stock is overvalued - investors are accepting too little return for the risk they're taking, which means they've bid the price too high. Short-selling such a stock makes sense because you expect the market to eventually correct this mispricing. As investors recognize the inadequate return relative to risk, they'll demand higher returns, which can only happen if the stock price falls. This is exactly what choice D describes - the stock is overvalued and its price should decrease as its return adjusts upward toward the SML. Choice A incorrectly suggests the stock is undervalued when it's actually overvalued. Choice B misunderstands that the SML focuses on systematic risk (beta), not unsystematic risk, and systematic risk is already being priced. Choice C incorrectly assumes negative beta, but a stock below the SML could have any beta value - the issue is that its return is too low for whatever beta it has. Remember this pattern: below the SML means overvalued (short opportunity), above the SML means undervalued (buy opportunity). The SML shows fair pricing based on systematic risk.

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