ESG Investing — Assignment 3

(a) Company A pressures suppliers for lower prices and longer payment terms.

The conflict is between shareholders (who demand higher margins) and suppliers. The company extracts value from suppliers — lower input prices and extended payables raise the firm's margin but shift cost and cash-flow risk onto suppliers, potentially squeezing their viability and working capital.

(b) Company B cuts corners on product quality and safety to prioritise sales and profit.

The conflict is between shareholders and customers (and, where injuries occur, the community). Short-run shareholder value is pursued at the direct expense of customer safety and welfare.

(c) Company C lobbies against new environmental laws or relocates to weaker-oversight jurisdictions to avoid regulation and tax.

The conflict is between shareholders and regulators / community / environment. Shareholder return is maximised by weakening or evading the rules that protect the community and the environment; externalised environmental and fiscal costs are borne by society, not the firm.

(d) A manager at Company D manipulates financial reports to show better short-term results to secure a larger bonus or promotion.

The conflict is between managers and shareholders (and creditors/regulators who rely on the reports). The manager pursues personal compensation at the expense of honest information; investors and creditors are misled, destroying long-run value and undermining capital-market integrity.

(e) Shareholders of Company E push for immediate cost cuts and higher dividends, discouraging investment in employee training.

The conflict is between shareholders and employees/management. Shareholder extraction of near-term cash at the expense of human-capital investment harms employee development, retention and long-run productivity.

The statement is incorrect. Conflicts exist within stakeholder groups as well as across them.

(a) A large shareholder arranges the company to buy goods/services from another business they own at inflated prices. This is a conflict within the shareholder group — the controlling shareholder's personal interest (the affiliate's profit) is opposed to the interest of the company's shareholders as a whole. It is related-party self-dealing that transfers value out of the listed company.

(b) Top managers cut employee benefits and lay off staff to boost quarterly profits and secure their own bonuses. This is a conflict within the management/employee group — the compensation of top executives is pursued by degrading the welfare of their fellow employees.

Conflicts of interest are a root cause of agency problems: managers or controlling shareholders acting in their own interest can lead to value-destroying decisions, excessive risk-taking, empire-building, related-party extraction and opaque reporting. Dispersed investors bear the downside.

Corporate governance mitigates them by:

• Aligning incentives — performance-linked, long-vesting compensation so managers gain from firm value creation.
• Strengthening board oversight — independent non-executive directors, separation of chairman/CEO, effective challenge of management.
• Dedicated committees — audit, remuneration, nomination and ESG committees with independent chairs.
• Transparency and accountability — independent external audit, reliable disclosure, whistleblower protections, personal accountability of the CEO for misstated reporting (e.g. dismissal for greenwashing).
• Protecting minority rights — equal voting, independent channels to raise concerns, rules against self-dealing.

Answer B. Align stakeholders' interests to support sustainable growth in firm value. 協調各利益相關者嘅利益，支持企業價值可持續增長。

A is wrong: governance seeks fair treatment, not preferential treatment of minorities.

C is wrong: conflicts cannot be fully eliminated; governance manages and aligns them.

D is wrong: governance does not eliminate business risk or guarantee against loss.

Best (a) — uniquely combines incentive alignment (compensation tied to environmental outcome over a multi-year horizon) with reporting accountability (personal dismissal for greenwashing). The CEO both wants to achieve the target and fears the consequences of misrepresenting it.

Answer C. An independent director challenges the CFO about unexplained reporting discrepancies and requires an external auditor to investigate.

(a) Board size, non-executive ratio, female ratio, nationality distribution 董事會規模、非執行比例、女性比例、國籍分佈

• Board size: 9
• Non-executive director ratio: 5/9 = 55.6%
• Female director ratio: 4/9 = 44.4%
• Nationality: USA 5 (55.6%), India 1, UK 1, China 1, Brazil 1 (11.1% each)

(b) Can you determine the independent director ratio? 可確定獨立董事比例嗎？

No. A non-executive director need not be independent — they may still have a material business or familial relationship with the company (e.g. former employee, significant shareholder, partner of a major client). Independence requires disclosure of outside affiliations and application of independence criteria; that information is not present in the data.

(c) Is there CEO–chair duality? What other concern arises? 有無 CEO-主席雙重角色？另有甚麼顧慮？

The data show no separate CEO — the chairman also serves as CFO. This is not the textbook CEO–chair duality (the chair is not the chief executive), but it is a serious concentration of power: the chairman is himself an executive officer. Because the chair is the CFO, the person who should provide independent oversight of management is the officer responsible for the firm's financial reporting. The chairman cannot independently challenge the very function (financial reporting) he controls, and there is no separate CEO line of accountability. This undermines both the independence of the board chair and the segregation of duties over financial reporting.

(d) Does a larger, more diverse, or more independent board necessarily perform better? 較大、更多元或更獨立嘅董事會是否必然表現更好？

No. Necessary but not sufficient. Board effectiveness depends on quality of deliberation and challenge, access to accurate information, the chair's ability to direct the agenda, presence of relevant expertise, and the board's actual willingness and power to hold management to account. Poorly constituted large boards can be just as ineffective as smaller ones.

(a) Total exercise payoff as a function of share price P 總行權收益作為股價 P 嘅函數

Zero for P ≤ $30; for P > $30 the payoff is $10,000 × (P − $30). Total premium to exercise = 10,000 × $30 = $300,000.

(b) Alignment and incentive problems 對齊及激勵問題

Alignment: option value is monotonic in P; CEO benefits only if P exceeds $30 strike. The grant aligns CEO's interest with shareholders in raising firm value.

Undesirable behaviour:

• Excessive risk-taking — payoff is convex (CEO captures all upside, downside capped at zero), giving a "lottery-ticket" incentive, especially near maturity or deep OTM.
• Short-termism / share-price manipulation — incentive to boost share price near the vesting/exercise window (buybacks, earnings management).
• Asymmetric incentive — CEO bears no personal loss from poor performance once strike is not met; no downside discipline.

Mitigate via long vesting, performance conditions, claw-backs.

(a) Conflicts of interest concern investors because they can lead to value-destroying corporate decisions. — True. 利益衝突引起投資者關注正正因為可導致破壞價值嘅公司決策。

(b) A higher ratio of independent directors typically improves board effectiveness. — Broadly true, with a limit. Generally associated with stronger oversight, but not monotonic — over-dominance of independents without management/industry competence can reduce effectiveness. 大致正確，但有局限。一般與較強監督相關，但非單調——獨立董事過多而無管理／行業能力可反降低效能。

(c) Good corporate governance reduces systematic risk by mitigating market crash potential. — False. Governance addresses internal idiosyncratic risk, not systematic (market) risk, which is macro and cannot be mitigated by any single firm. 錯誤。管治處理內部特有風險，非系統性（市場）風險，後者係宏觀，任何單一公司均無法消除。

(d) Information asymmetry means investors have more information than managers. — False. Reversed. Managers observe operations internally and hold more information than dispersed investors. 反轉。管理層內部監察營運，掌握比分散投資者更多資訊。

Answer B. Excessive risk-taking by management. Poor governance weakens oversight and accountability, permitting managers to take excessive risk, engage in self-dealing or pursue empire-building. (A and D are features of good governance; C is a reduction in agency costs, i.e. an improvement.)

Answer B. The CEO benefits from a higher share price when that price exceeds the strike price.

Answer B. Overseeing internal and external audits and financial compliance.

Answer A. Common stocks represent ownership in a public company.

B false — no maturity date; contributed capital is not repayable on any specified date (that is a feature of debt).

C false — common stock is a high-risk investment; shareholders are residual claimants bearing the largest risk.

D false — dividends are not an unconditional obligation; paid at the board's discretion, not contractual.

(a) Cash flows and discount rate 現金流及貼現率

• CFₜ: the investor's expected future dividends (+ terminal/liquidation value). These are the investor's relevant cash flows, not the firm's free cash flow to the enterprise.
• r_E: the investor's required rate of return, compensating for both economic risk (business and market risk) and ESG risk (environmental, social and governance risks to which the firm is exposed).

(b) How economic and ESG factors affect fair value 經濟及 ESG 因素如何影響公允價值

ESG factors enter via two channels: (i) cash-flow channel — material ESG risks (regulatory carbon costs, litigation, resource depletion, labour disputes, governance failures) alter the level and timing of expected CFs (e.g. stranded-asset write-offs, fines). (ii) discount-rate channel — ESG risk is part of total risk; higher ESG-risk exposure raises required return r_E and lowers fair value. Strong, credibly managed ESG lowers the risk premium and supports durable cash flows, raising fair value.

(c) Using estimated fair value 使用估計公允價值

Compare estimated intrinsic (fair) value with prevailing market price: if market price < fair value → undervalued (potential buy, margin of safety); if market price > fair value → overvalued (potential sell/avoid). The margin of safety is the decision rule.

(a) Return in each state and expected return 各狀態回報及期望回報

• Boom: r = 12/10 − 1 = +20%
• Recession: r = 9/10 − 1 = −10%
• E[r] = 0.5(+20%) + 0.5(−10%) = +5%

(b) Realised return if price is $12 若實際股價為 $12，實際回報

Realised return = +20%. It differs from the expected return of +5% because the expected return is the probability-weighted average across all possible states (ex-ante), whereas the realised return is the single outcome that actually occurred (ex-post). The −10% recession outcome did not materialise.

• E[A] = 0.3(0.50) + 0.6(0.10) + 0.1(−0.30) = 0.15 + 0.06 − 0.03 = 0.18 (18%)
• E[B] = 0.3(0.02) + 0.6(0.08) + 0.1(0.25) = 0.006 + 0.048 + 0.025 = 0.079 (7.9%)
• E[ESG] = 0.3(0.30) + 0.6(0.15) + 0.1(0.10) = 0.09 + 0.09 + 0.01 = 0.19 (19%)
• E[F] = 0.05 (5%), constant across states.

Not correct as an absolute statement. Under risk-aversion, investors require a risk premium for bearing additional risk, so riskier assets are expected to offer higher returns. But: (i) this holds in expectation, not for any particular realisation; (ii) it is not a law — some risky assets may not compensate; (iii) "risk" must be correctly measured (total vs systematic) — a high-volatility asset may have much of its risk diversifiable. The correct statement: higher expected return is generally required for bearing higher risk, not that it must be earned.

• Long A: 1,000 × $30 = $30,000
• Short F: 10 × $1,000 = $10,000 (proceeds finance part of the shares)
• Net equity = $30,000 − $10,000 = $20,000

Weights sum to +1.00. The negative weight on F is a short position: the investor has borrowed cash (effectively at the T-bill rate) to finance the over-investment in A. Gross exposure $40,000 on $20,000 equity = 2× leverage. The net position is leveraged long in A.

(a) Cash profit or loss 現金盈虧

If P₁ < P₀ (price fell) the seller profits; if P₁ > P₀ the seller loses.

(b) Return relative to initial sale proceeds and to margin capital M₀ 相對初始賣出所得及按金 M₀ 嘅回報

Relative to P₀: return = (P₀ − P₁)/P₀ = −r, the negative of the long return on the full notional.

Relative to margin capital M₀ (< P₀): return = (P₀ − P₁)/M₀ — the same sign but magnified on a smaller base. A short position carries greater percentage risk on the investor's own capital than the long equivalent.

(a) Portfolio weights and expected return 組合權重及期望回報

• Value of A: $20,000; Value of B: $80,000; Total: $100,000
• w_A = 0.20, w_B = 0.80
• E[R_p] = 0.20(0.18) + 0.80(0.079) = 0.036 + 0.0632 = 0.0992 (9.92%)

(b) Portfolio return in each state 各狀態嘅組合回報

Verify: E[R_p] = 0.3(0.116) + 0.6(0.084) + 0.1(0.14) = 0.0348 + 0.0504 + 0.014 = 0.0992 (9.92%) ✓ identical to (a).

No. Portfolio σ is generally less than the value-weighted average of individual σs (equal only at ρ=+1). Portfolio risk is governed by covariances, not merely individual variances. Because cross-covariances are typically below the product of individual σs, diversification reduces portfolio risk. The weighted average is an upper bound, attained only at perfect positive correlation.

From R_p = [0.116, 0.084, 0.14], E[R_p] = 0.0992:

Weighted average of individual σs = 0.20(0.24) + 0.80(0.0630) = 0.048 + 0.0504 = 0.0984 (9.84%)

Portfolio σ (1.97%) is far below the weighted average (9.84%) — a large diversification benefit of 0.0786, because A and B are strongly negatively correlated (ρ[A,B] ≈ −0.92), so their returns offset one another across states.

Answer B. "Zero correlation establishes that there is no causal relationship between two variables."

Zero correlation means no linear association; it does not establish the absence of a causal relationship (which may be non-linear), and correlation in general does not establish causation.

Covariance matrix 協方差矩陣

Correlation matrix 相關係數矩陣

Entries that cannot be defined: every correlation involving T-bill F is undefined, because σ[F] = 0. The correlation ρ = Cov/(σ_i σ_j) has a zero denominator for any pair involving F. The T-bill is deterministic — no co-movement to measure.

(a) Expected return is formed before the fact, and realised return is calculated after the fact. — True. 期望回報係事前概念，實際回報係事後計算。

(b) Diversification means portfolio risk is lower than the risk of every individual asset in the portfolio. — False. Diversification means portfolio risk is lower than the weighted average of individual risks (when correlations < 1). Not necessarily lower than every single constituent. 分散化指組合風險低於個別風險之加權平均（相關<1時），並非必然低於每一個個別成分。

(c) Covariances between assets become more important to portfolio risk as the number of assets becomes large. — True. As N grows, individual variances are scaled by 1/N and diversified away; portfolio variance converges to the average covariance. 當 N 增大，個別方差被 1/N 縮小並被分散；組合方差趨近於平均協方差。

Answer B. 20% in A and 80% in B.

Answer Stock B.

The most negatively correlated asset offsets the long X holder's losses when X falls, reducing total portfolio volatility. A and D, being positively correlated with X, would add risk; C offers little as it is essentially uncorrelated.

(a) Mechanical application of σ_p² = w'Σw 機械套用組合方差公式

(b) Validity check 有效性檢定

The matrix cannot represent valid variances and covariances. Necessary condition: every implied pairwise correlation ∈ [−1, 1]. Here:

• ρ_XZ = 0.0350 / √(0.02 × 0.01) = 0.0350 / 0.01414 ≈ 2.475 > 1 — impossible
• ρ_YZ = 0.0250 / √(0.05 × 0.01) = 0.0250 / 0.02236 ≈ 1.118 > 1 — impossible

A valid covariance matrix must be positive semi-definite; this one has det < 0, confirming it is not PSD. The mechanical σ_p = 17% is spurious.

Sample statistics (n = 5):

• Sample mean = (7.25 + 3.75 + 1.25 + 5.00 + 2.50)/5 = 3.95%
• Sample variance = Σ(R_t − R̄)²/(n−1) = 0.0005356
• Sample standard deviation = √0.0005356 ≈ 2.31%

• Individual stocks (4): Microsoft (MSFT), Apple (AAPL), JPMorgan Chase (JPM), Exxon Mobil (XOM)
• Benchmarks (2): S&P 500 Index (^GSPC) and the iShares MSCI USA ESG Screened ETF (DIV), used as investable proxy for an ESG benchmark
• Sample period: calendar years 2016–2024 (annual, 9 observations)
• Currency: USD
• Data source: Yahoo Finance (yfinance), split- and dividend-adjusted closing prices
• Return convention: annual total-return holding-period return from split- and dividend-adjusted year-end closes: r_t = P_t / P_{t−1} − 1. Splits and distributions are embedded in the adjusted series, so each annual return captures both price appreciation and distributions.

Year-end adjusted closes (USD) 年末調整後收市價（美元）

Annual total returns 年度總回報

COVARIANCE.S(MSFT, DIV) = 0.01010124

CORREL(MSFT, DIV) = 0.2360

Sample variance–covariance matrix (four stocks) 樣本協方差矩陣

Sample correlation matrix 樣本相關係數矩陣

Annual portfolio returns 年度組合回報

• Sample mean = 0.248735 (24.87%)
• Sample variance (direct) = 0.02722784
• Sample variance (w'Σw) = 0.02722784 — identical, confirming internal consistency
• Sample standard deviation = 0.165009 (16.50%)

Diversification effect 分散化效應

The equal average of the four stocks' individual standard deviations is:

The portfolio's σ (16.50%) is 15.16 percentage points lower than the weighted average of individual σs. This diversification benefit arises because the constituents are not perfectly positively correlated: notably, XOM is negatively correlated with both MSFT (ρ ≈ −0.54) and AAPL (ρ ≈ −0.59), so energy and technology return streams offset one another across years. The portfolio achieves a higher mean return (24.87%) at roughly half the volatility of the average single name, illustrating the core risk-reduction benefit of holding a diversified, non-perfectly-correlated set of assets.