Corporate_finance_and_portfolio_management

Content

[TOC]

corporate governance and ESG

ESG: environmental, social and governance

  • stakeholder: 利益者相关理论

  • shareholder

company stakeholders

stakeholder groups

  • shareholders: controlling/minority

  • creditors

  • managers and employees

  • board of directors

  • customers

  • suppliers

  • governments/regulators

principal-agent and other relationship in corporate governance

  • shareholder and manger/director relationships

  • controlling and minority shareholder relationships

    • straight voting: one vote for each share owned

  • manager and board relationship

  • shareholder versus creditor interests: growth versus default risk

  • other stakeholder conflicts

    • customers and shareholders

    • customers and suppliers

    • shareholders and governments or regulators

stakeholder management

stakeholder: the identification, prioritization, and understanding of the interests of stakeholder groups, and managing the company's relationships with groups

  • legal infrastructure

  • contractual infrastructure

  • organizational infrastructure

  • governmental infrastructure

general meetings

  • annual general meeting (AGM): ordinary resolution, external auditors and performance overview

  • extraordinary general meetings (EGM): special resolution, significant changes to a company such as bylaw amendments

  • proxy voting

  • cumulative voting: as opposed to straight voting

board of directors and committees

staggered boards: 分期分级董事会

board of directors committees

  • audit committee

  • governance committee

  • remuneration or compensation committee

  • nomination committee

  • risk committee

  • investment committee

factor affecting stakeholder relationships and corporate governance

market factors

  • shareholder engagement

  • shareholder activism

  • competition and takeovers

non-market factors

  • legal environment

  • the media

  • the corporate governance industry

corporate governance and stakeholder management risks and benefits

risk of poor governance and stakeholder management

  • weak control system

  • inefficient decision making

  • legal, regulatory and reputational risks

  • default and bankruptcy risks

benefits of effective governance and stakeholder management

  • operational efficiency

  • improved control

  • better operating and financial performance

  • lower default risk and cost of debt

analyst considerations in corporate governance and stakeholder management

economic ownership and voting control

  • dual class structure: one class of share may be entitled to several votes per share while another is entitled to one vote per share

board of directors representation

remuneration and company performance

  • concerns if cash-based only, without an equity component, which indicates misalign between management and other stakeholders

investors in the company

strength of shareholders' rights

managing long-term risks

ESG considerations for investors

ESG integration is also termed sustainable investing or responsible investing and sometimes socially responsible investing

ESG implementation methods

  • negative screening: excludes certain sectors, companies that violate accepted standards in such area as human rights or environmental concerns

  • positive screening and best-in-class: focus on investments with favorable ESG aspects

  • thematic investing: typically consider a single factor, such as energy efficiency or climate change.

capital budgeting

capital budgeting process steps:

  • step 1: idea generation

  • step 2: analyzing project proposal

  • step 3: create the firm-wide capital budget

  • step 4: monitoring decision and conduction a post-audit.

categories of capital budgeting projects

  • replacement projects

  • expansion projects

  • new products ans services

  • regulatory, safety and environmental projects

  • other

basic principles of capital budgeting

  • decisions are based on cash flows, not accounting income

    • sunk cost

    • opportunity cost

    • incremental cash flow: is the cash flow that is realized because of a decision, several types of project interactions make the incremental cash flow analysis challenging:

      • independent projects v.s. mutually exclusive projects

      • project sequencing

      • unlimited funds v.s. capital rationing

    • externality: is the effect of an investment on other things besides the investment itself such as cannibalization (自相残杀)

    • conventional cash flows v.s. nonconventional cash flows

  • timing of cash flows is crucial

  • cash flows are based on opportunity costs

  • cash flows are analyzed on an after-tax basis

  • financing costs are ignored

investment decision criteria

net present value (NPV)

NPV=∑t=1nCFt(1+r)t−OutlayNPV = \sum_{t=1}^{n} \frac{CF_t}{(1+r)^t} - Outlay

Invest if NPV > 0; Do not invest if NPV < 0

internal rate of return (IRR)

∑t=1nCFt(1+IRR)t=Outlay\sum_{t=1}^{n} \frac{CF_t}{(1+IRR)^t} = Outlay

Invest if IRR > r; Do not invest if IRR < r

payback period (PBP)

PBP is the number of years it takes to recover the initial cost of an investment PBP = full years until recovery + (unrecovered cost at the beginning of the last year)/(cash flow during the last year)

discounted payback period

discounted payback period uses the present value pf the project's estimated cash flows.

Average accounting rate of return

ARR = Average net income/Average book value

profitability index (PI)

The profitability index is the present value of a project's future cash flows divided by the initial cash outlay:

PI=PV of future cash flowsCF0=1+NPVCF0PI = \frac{PV\ of\ future\ cash\ flows}{CF_0} = 1 + \frac{NPV}{CF_0}

IF PI>1.0, accept the project; if PI<1.0, reject the project

compare the NPV and IRR methods

The rate at which the NPVs are equal for two projects is called the crossover rate.

A key advantage of NPV is that it is a direct measure of the expected increase in the value of the firm. NPV is the theoretically the best method. Its main weakness is that it does not include any consideration of the size of the project.

A key advantage of IRR is that it measures profitability as a percentage, showing the return on each dollar invested. IRR provides information on the margin of safety that the NPV does not. The disadvantage of the IRR method are 1) the possibility of the producing rankings of mutually exclusive projects different from those from NPV analysis and 2) the possibility that a project has multiple IRR or no IRR.

cost of capital

weighted average cost of capital: a weighted average of the aftertax required rates of return on a company's common stock, and long-term debt, where the weights are the fraction of each source of financing in the company's target capital structure.

WACC=wdrd(1−t)+wprp+wereWACC = w_d r_d (1-t) + w_p r_p + w_e r_e where $w_d$ = the proportion of the debt that the company uses when it raises new funds $r_d$ = the before-tax marginal cost of debt $t$ = the company's marginal tax rate $w_p$ = the proportion of preferred stock the company uses when it raises new funds $r_p$ = the marginal cost of the preferred stock $w_e$ = the proportion of equity that the company uses when it raises new funds $r_e$ = the marginal cost of equity

cost of debt

P0=(∑t=1nPMTt(1+rd)t)+FV(1+rd)nP_0 = \left(\sum_{t=1}^n \frac{PMT_t}{(1+r_d)^t}\right) + \frac{FV}{(1+r_d)^n}

  • debt-rating approach: estimates the before-tax cost of debt by using the yield on comparable rated bonds for maturities that closely match that of the company's existing debt.

cost of preferred stock

rp=DpPpr_p = \frac{D_p}{P_p}

where $P_p$ = the current preferred stock price per share $D_p$ = the preferred stock dividend per share $r_p$ = the cost of the preferred stock

cost of common equity

capital asset pricing model approach

E(Ri)=RF+βi[E(RM)−RF]E(R_i) = R_F + \beta_i [E(R_M) - R_F] where $\beta_i$ = the return sensitivity of stock i to changes in the market return $E(R_M)$ = the expected return on the market $E(R_M) - R_F$ = the expected market risk premium

historical equity risk premium approach

This approach requires compiling historical data to find the average rate of return of a country's market portfolio and the average rate of return for the risk -free rate in the country.

dividend discount based model approach

P0=D1re−gP_0 = \frac{D_1}{r_e - g} where $P_0$ is the current market value of the equity market index $D_1$ are the dividends expected next period on the index $r_e$ is the required rate pf return on the market $g$ is the expected growth rate of dividends thus, we got

re=D1/P0+gr_e = D_1/P_0 + g

this is consistent with what is expressed in Gordon growth model To estimate the sustainable growth rate, the relationship can be given as: g=(1−D/EPS)ROEg = (1 - D/EPS)ROE The term (1-D/EPS) is the company's earnings retention rate.

bond yield plus risk premium approach

re=rd+risk premiumr_e = r_d + risk\ premium

estimating beta and determining a project beta

One common method of estimating the company's stock beta is to use a market model regression of the company's stock returns ($Ri$) against market returns ($R_m$) over T period $$R{it} = \hat{a} + \hat{b} R_{mt}\qquad t = 1,2,\dots T$$

  • pure-play method: A method for estimating the beta for a company or project; it requires using a comparable company's beta and adjusting it for financial leverage differences.

To get the asset beta for a publicly traded firm, we use the following formula:

βasset=βdebtwd+βequitywe\beta_{asset} = \beta_{debt} w_d + \beta_{equity} w_e or

βasset=βdebt(DD+E)+βequity(ED+E)\beta_{asset} = \beta_{debt} \left(\frac{D}{D+E}\right) + \beta_{equity} \left(\frac{E}{D+E}\right)

But interest on debt is deducted by the company to arrive at taxable income, so the claim that creditors have on the company's assets does not cost the company the full amount but, rather, the after-tax claim:

βasset=βdebt((1−t)D(1−t)D+E)+βequity(E(1−t)D+E)\beta_{asset} = \beta_{debt} \left(\frac{(1-t)D}{(1-t)D+E}\right) + \beta_{equity} \left(\frac{E}{(1-t)D+E}\right)

We generally assume that a company's debt does not have market risk, so $\beta_{debt}$ = 0, then

βasset=βequity(E(1−t)D+E)=βequity[11+(1−t)DE]\beta_{asset} = \beta_{equity} \left(\frac{E}{(1-t)D+E}\right) = \beta_{equity} \left[\frac{1}{1+(1-t)\frac{D}{E}}\right]

So we can assume the beta of the project $\beta_{U, comparable}$ by using:

βU,comparable=βL,comparable[11+(1−tcomparable)DcomparableEcomparable]\beta_{U, comparable} = \beta_{L, comparable} \left[\frac{1}{1+(1-t_{comparable})\frac{D_{comparable}}{E_{comparable}}}\right]

We then consider the financial leverage of the project or company and calculate its equity risk, $\beta_{L, project}$:

βL,project=βU,comparable[1+(1−tproject)DprojectEproject]\beta_{L, project} = \beta_{U, comparable} \left[1+(1-t_{project})\frac{D_{project}}{E_{project}}\right]

uses of country risk premiums in estimating the cost of equity

The country risk premium (CRP) can be calculated as: CRP = sovereign yield spread (annualized std of equity index of developing country/ annualized std of *sovereign bond market in terms of the developed market currency)

marginal cost of capital schedule

Marginal cost of capital (MCC) is the cost of the last new dollar of capital a firm raises. The MCC shows the WACC for different amounts of financing. The amount of capital at which the weighted average cost of capital changes -- which means that the cost of one of the source of capital changes -- is referred to as a break point. The break point is calculated as: break point = amount of capital at which the component's cost of capital changes/weight of the component in the capital structure

Flotation costs

flotation costs: fees charged to companies by the investment bankers and other costs associated with raising new capital

As an amount per share or as a percentage of the share price. With flotation costs in monetary terms on a per share basis, F, the cost of external equity is

re=D1P0−F+gr_e = \frac{D_1}{P_0 - F} + g

or

re=D1P0(1−f)+gr_e = \frac{D_1}{P_0(1 - f)} + g

miscellaneous

  • estimates the weight of the debt and equity by forecasted market value

  • Asset risk does not change with a higher debt-to-equity ratio. Equity risk rises with higher debt.

corporate finance

measures of leverage

  • business risk: refers to the risk associated with a firm's operating income and is the result of uncertainty about a firm's revenues and the expenditures necessary

    • sales risk: is the uncertainty about the firm's sales

    • operating risk: refers to the additional uncertainty about operating earnings caused by fixed operating costs. The greater the proportion of fixed costs to variable costs, the greater a firm's operating risk.

      DOL (degree of leverage) = Percentage change in operating income (EBIT) / percentage change in units sold = $\Delta EBIT/EBIT/(\Delta Q/Q)$

      operating income = number of units sold *[price per unit - variable cost per unit] - fixed operating costs

      Thus, we have

      DOL=Q(P−V)Q(P−V)−F=S−TVCS−TVC−FDOL = \frac{Q(P - V)}{Q(P - V) - F} = \frac{S - TVC}{S - TVC - F}

      where

      Q = quantity of units sold

      P = price per unit

      V = variable cost per unit

      F = fixed costs

      S = sales

      TVC = total variable cost

  • financial risk: refers to the additional risk that the firm's common stockholders must bear when a firm uses fixed cost (debt) financing.

    DFL (degree of financial leverage) = percentage change in net income (EPS)/ percentage change in operating income (EBIT)

$$DFL = \frac{ [Q(P-V) - F] (1 - t) }{[Q(P-V) - F - C] (1 - t)} = \frac{ [Q(P-V) - F]  }{[Q(P-V) - F - C] }$$

where
C = fixed financial cost
t = tax rate

total leverage

DTL (degree of total average) = Percentage change in net income / Percentage change in the number of units sold = (Percentage change in net income / percentage change in units sold) $\times$ (percentage change in net income (EPS)/ percentage change in operating income) = $DOL \times DFL$

DTL=DOL×DFL=%ΔEBIT%Δsales×%ΔEPS%ΔEBIT=Q(P−V)[Q(P−V)−F]×[Q(P−V)−F][Q(P−V)−F−C]=Q(P−V)[Q(P−V)−F−C]DTL = DOL \times DFL = \frac{\%\Delta EBIT}{\%\Delta sales} \times \frac{\%\Delta EPS}{\%\Delta EBIT} = \frac{ Q(P-V) }{[Q(P-V) - F ] } \times \frac{ [Q(P-V) - F] }{[Q(P-V) - F - C] } = \frac{ Q(P-V) }{[Q(P-V) - F - C] }

breakeven point

breakeven point

The breakeven point $Q{BE}$ is the number of units produced and sold at which the company's net income is zero, since NI=PV−QV−F−CNI = PV - QV - F - C so when NI = 0, we have $$Q{BE} = \frac{F + C}{P - V}$$

operating breakeven point

When $PQ{OBE} = VQ{OBE} + F$, we get QOBE=FP−VQ_{OBE} = \frac{F}{P - V}

dividends and share repurchases

See reference on mbalib

  • regular dividends: occur when a company pays out a portion of profits on a consistent schedule

    • open-market DRPs (dividend reinvestment plans) in which the company purchases shares in the open market to acquire the additional shares credited to plan participants

    • new issue DRPs (scrip dividend schemes in UK) in which the company meets the need for additional shares by issuing them instead of purchasing them

  • special dividends: are used when favorable circumstances allow the firm to make a one-time cash payment to shareholders, in addition to any regular dividends the firm pays

  • liquidating dividends: occur when a company goes out of business and distributes the proceeds to shareholders.

  • stock dividend: a stock dividend is accounted for as a transfer of retained earnings to contributed capital

  • stock split: stock splits are similar to stock dividends in that they have no economic effect on the company and shareholders' total cost basis does not change.

  • 选择股票拆分和股票红利的前五位原因是:为了保存现金;因为税收原因而更加吸引投资者;增加股东数目;股票价格不会在除权日完全调整;增加股东信心

    1. 股票股利 stock dividend，是指股份公司对原有股东采取无偿派发股票的行为。送股时，将上市公司的留存收益转入股本账户，留存收益包括盈余公积和未分配利润，现在的上市公司一般只将未分配利润部分送股。

    2. 转增股是指上市公司将公司的资本公积金转化为股本的形式赠送给股东的一种分配方式。

    3. 股份拆分 stock split，也就是股票分割（stock spilt）又称股票拆细或拆股，股票分割是比较技术的说法。股票分割是指即将一张较大面值的股票拆成几张较小面值的股票。 股票分割对公司的资本结构不会产生任何影响，一般只会使发行在外的股票总数增加，资产负债表中股东权益各账户（股本、资本公积、留存收益）的余额都保持不变，股东权益的总额也保持不变。

dividends: payment chronology

  • declaration date: the date the board of directors approves payment of the dividend.

  • Ex-dividend date: the first day a share of stock trades without the dividend. The ex-dividend date is also the cutoff date for receiving the dividend and occurs two business days before the holder-of-record date. If you buy the share on or after the ex-dividend date, you will not receive the dividend. You can receive the dividend if you buy the stock the day before ex-dividend date.

  • holder-of-record date: the date on which the shareholders of record are designated to receive the dividend

  • payment date: the date the dividend checks are mailed out or when the payment is electronically transferred to shareholder account.

compare share repurchase methods

A share repurchase is a transaction in which a company buys back shares of its own common stock. 1. buy in the open market 2. buy a fixed number of share at a fixed price 3. Dutch auction 3. repurchase by direct negotiation

  • A share repurchase using borrowed funds will increase EPS if the after-tax cost of debt used to buy back shares is less than the earning yield of the shares before the repurchase.

  • BVPS will decrease if the repurchase price is greater than the original BVPS and increase if the repurchase price is less than the original BVPS

  • Assuming the tax treatment of the two alternatives is the same, a share repurchase has the same impact on shareholder wealth as a cash dividend payment of an equal amount.

working capital management

primary and secondary source of liquidity and factors that influence a company's liquidity position

  • primary sources of liquidity: are the sources of cash it uses in its normal day-to-day operations.

  • secondary sources of liquidity: include liquidating short-term or long-lived assets, negotiating debt agreements, of filing for bankruptcy and reorganizing the company.

factors that influence a company's liquidity position

  • drags on liquidity: delay or reduce cash inflows

  • pulls on liquidity: accelerate cash outflows

compare a company's liquidity measures with those of peer companies

  • current ratio is the best-known measure of liquidity:

    current ratio = current asset / current liabilities

  • quick ratio or acid-test ratio is a more stringent measure of liquidity because it does not include inventories and other assets that might not be very liquid:

    quick ratio = (cash + short-term marketable securities + receivables)/ current liabilities

  • a measure of accounts receivable liquidity is the receivables turnover:

    receivable turnover = credit sales / average receivables

  • inverse of the receivables turnover multiplied by 365 is the number of days of sales outstanding

  • a measure of a firm's efficiency with respect to its processing and inventory

    inventory turnover = COGS / average inventory

  • average inventory processing period or number of days of inventory

  • a measure of the use of trade credit by the firm is the payable turnover ratio:

    payables turnover ratio = purchase / average trade payables

  • operating cycle, the average number of days that it takes to turn raw materials into cash proceeds from sale, is:

    operating cycle = days of inventory + days of receivables

  • cash conversion cycle or net operating cycle is the length of time it takes to turn the firm's cash investment in inventory back into cash, in the collections from the sales of that inventory.

    cash conversion cycle = average days of receivables + average days of inventory - average days of payables

managing the cash position

cash forecasting system

item

short term

medium term

long term

data frequency

daily/weekly for 4-6 weeks

monthly for one year

annually for 3-5 years

format

receipts and disbursements

receipts and disbursements

projected financial statements

techniques

simple projections

projection models and averages

statistical models

accuracy

very high

moderate

lowest

reliability

very high

fairly high

not as high

uses

daily cash management

planning financial transactions

long-range financial position

yields on short term investment

  • discount interest: difference between the purchase price and the face value

  • money market yield: a yield on a basis comparable to the quoted yield on an interest-bearing money market instrument that pays interest on a 360-day basis

    money market yield = (face value - purchase price)/purchase price * (360/number of days to maturity)

    bond equivalent yield = (face value - purchase price)/purchase price * (365/ number of the maturity)

    discount-basis yield = (face value - purchase price)/face price * (360/ number of the maturity)

investment risk

  • credit (or default) risk

  • market (or interest rate) risk

  • liquidity risk

  • foreign exchange

float factor = average daily float / average daily deposit = average daily float / (total amount of checks deposited/ Number of days)

the economics of taking a trade discount

cost of trade credit=(1+Discount1−Discount)(365/number of days beyond discount period)−1cost\ of\ trade\ credit = (1+\frac{Discount}{1 - Discount})^{(365/number\ of\ days\ beyond\ discount\ period)} - 1 where: number of days beyond discount period = number of days after the end of the discount period

evaluating accounts payable management

Number of days of payables = accounts payable / average's purchases where: average's purchase = annual purchase / 365

managing short-term financing

source of short-term funding from banks

lines of credit: 信用额度

  • uncommitted line of credit： typically for large corporations

  • committed (regular) line of credit

  • revolving line of credit: 循环信贷

  • collateralized loan

  • discounted receivable

  • banker's acceptance factoring: 银行承兑

nonbank source of short-term funding

  • nonbank finance companies

  • commercial paper: 商业票据，无抵押短期债务，一般低于当时市场利率

cost of borrowing

The cost of the line of credit: Cost=Interest+Commitment feeLoan amountCost = \frac{Interest + Commitment\ fee}{Loan\ amount}

If the interest rate is stated as "all inclusive", as may be the case in a banker's acceptance, the interest is compared with the net proceeds when determining the cost: Cost=InterestNet proceeds=InterestLoan amount−InterestCost = \frac{Interest}{Net\ proceeds} = \frac{Interest}{Loan\ amount - Interest}

If there are dealer's fees and other fees such as a backup fee, the cost is: Cost=Interest+Dealer′s commission+Backup costsLoan amount−InterestCost = \frac{Interest + Dealer's\ commission + Backup\ costs}{Loan\ amount - Interest}

1/10 net 30 It means if the bill is paid within 10 days, there is a 1% discount. Otherwise, the bill should be paid within 30 days.

portfolio management

portfolio approach to investing

diversification ratio

  • avoiding disaster

  • reduce risk

  • composition matter for the risk-return trade-off

  • not necessarily downside protection

  • the emergence of modern portfolio theory

type of investors and distinctive characteristics and needs of each

  • individual investors

    • defined contribution pension plan (DC plan): the contribution is defined while the future value is unknown

  • institutional investors

    • defined benefit pension plans (DB plan): the benefit is defined

    • endowments: is a fund that is dedicated to providing financial support on an ongoing basis for a specific purpose

    • foundation: is a fund established for charitable purpose to support specific types of activities or to fund research related to a particular disease.

    • banks

    • insurance

    • investment companies

    • sovereign wealth funds

steps in the portfolio management process

  1. planning step

    • understanding the client's needs

    • preparation of an investment policy statement (IPS)

IPS: a written planning document that describes a client's investment objective and risk tolerance over a relevant time horizon, along with constraints that apply to the client's portfolio.

  1. execution step

    • asset allocation

    • security analysis

    • portfolio construction

  2. feedback step

    • portfolio monitoring and rebalancing

    • performance measurement and reporting

mutual funds and other funds

  • mutual funds (as little as US$50)

  • Exchange traded funds

  • separately managed accounts (US$100,000)

  • hedge funds (US$1,000,000+)

  • private equity funds

  • open-end fund: accepts new investment money and issues additional shares at a value equal to the net asset value of the fund at the time of investment

  • closed-end fund: no new investment money is accepted. New investors invest by buying existing shares, and investors in the fund liquidate by selling their shares to other investors

  • no-load fund: no fee for investing and redeeming except for an annual fee

  • load fund: in addition to the annual fee, a percentage fee is charged to invest in the fund and/or for redemption from the fund

type of mutual funds

  • money market funds: invest in short-term debt securities and provide interest income with very low risk of changes in share value.

  • bond mutual funds: invest in fixed-income securities

  • stock mutual funds:

  • hybrid/balanced funds

other investment products

  • Exchange traded funds (ETFs): ETF是一种跟踪“标的指数”变化、且在证券交易所上市交易的基金。ETF，属于开放式基金的一种特殊类型，它综合了封闭式基金和开放式基金的优点，投资者既可以在二级市场买卖ETF份额，又可以向基金管理公司申购或赎回ETF份额，不过申购赎回必须以一篮子股票(或有少量现金)换取基金份额或者以基金份额换回一揽子股票(或有少量现金)

  • separately managed accounts: 专户理财

  • hedge funds

    • Global Macro: 全球宏观对冲策略

    • Emerging Markets: 新兴市场策略

    • Event Driven: 事件驱动策略

    • Equity Market Neutral: 股票市场中性策略

    • Dedicated Short Bias: 股票放空策略

    • Managed Futures: 管理期货策略

    • Fixed Income Arbitrage: 固定收益套利策略

    • Convertible Arbitrage: 可转换债券套利策略

    • Long/Short Equity: 多/空仓策略

    • Multi-Strategy: 多重策略

  • buyout funds

  • venture capital funds

risk management

risk management process seeks to 1) identify the risk tolerance of the organization, 2) identify and measure the risks that the organization faces, and 3) modify and monitor these risks

an overall risk management framework encompasses several activities, including:

  • establishing process and policies for risk governance

  • determining the organization's risk tolerance

  • identifying and measuring existing risks

  • managing and mitigating risks to achieve the optimal bundle of risks

  • monitoring risk exposures over time

  • communicating across the organization

  • performing strategic risk analysis

risk governance

risk governance is the top-down process and guidance that directs risk management activities to align with and support the overall enterprise.

identification of risks

  • financial risks

    • market risk

    • credit risk

    • liquidity risk

  • non-financial risks

    • operational risk

    • solvency risk

    • regulatory risk

    • governmental or political risk

    • legal risk

    • model risk

    • tail risk

    • accounting risk

risk measurement

  • standard deviation

  • beta

  • duration

derivative risk

  • delta: this is the sensitivity of derivatives values to the price of the underlying asset

  • gamma: this is the sensitivity of delta to changes in the price of the underlying asset

  • vega: sensitivity of derivatives values to the volatility of the price of the underlying asset

  • rho: this is the sensitivity of derivatives values to changes in the risk-free rate

  • VaR (value at risk): 在险价值 $ VaR_{\alpha} = \inf \lbrace l \in \mathfrak{R} : P(L>l) \leq 1- \alpha \rbrace $

  • scenario analysis and stress testing both examine the performance of a portfolio subject to extreme events

  • self-insurance: an organization has decided to bear a risk, e.g. setting up a reserve fund to cover losses

  • risk transfer: for a risk an organization has decided not to bear, risk transfer or risk shifting can be employed e.g. buying insurance

  • fidelity bond: 雇员忠诚保险

  • surety bond: with a surety bond, an insurance company has agreed to make a payment if a third party fails to perform under the terms of a contract of agreement with organization.

risk tolerance -> risk budgeting -> risk exposure the choice of risk-modification method is based on weighing costs versus benefits in light of the entity's risk tolerance

portfolio risk and return

  • Holding period return (HPR)

    holding period return = end-of-period value/beginning-of-period value - 1 = $\frac{P_t + Div_t}{P_0} - 1 = \frac{P_t - P_0 + Div_t}{P_0}$

  • average return

    • arithmetic

      arithmetic mean return=R1+R2+⋯+Rnnarithmetic\ mean\ return = \frac{R_1 + R_2 + \dots + R_n}{n}

    • geometric mean return: compounds the returns instead of the amount invested. Basically, the geometric mean reflects a "buy-and-hold" strategy, whereas the arithmetic reflects a constant dollar investment at the beginning of each time period.

      geometric mean return=∏t=1T(1+Rit)T−1geometric\ mean\ return = \sqrt[T]{\prod_{t=1}^{T} (1+R_{it})} - 1

    • money-weighted rate of return is the internal rate of return on a portfolio based on all of its cash inflows and outflows, similar to internal rate of return and yield to maturity.

  • other return measures

    • gross return: total return on security portfolio before deducting fees for the management and administration of the investment account.

    • net return: refer to the return after these fee have been deducted.

    • pretax nominal return

    • after-tax nominal return

    • real return: is nominal return adjusted for inflation

      since $(1+r) = (1 + r_{rF})\times(1+\pi)\times(1+RP)$, so we have

      (1+rreal)=(1+rrF)×(1+RP)(1 + r_{real}) = (1 + r_{rF}) \times (1 + RP)

    • leveraged return

variance and covariance of returns

variance of a portfolio of assets

∑i=1Nwi=1\sum_{i=1}^N w_i = 1

σP2=Var(Rp)=Var(∑i=1NwiRi)\sigma_P^2 = Var(R_p) = Var(\sum_{i=1}^N w_i R_i)

σP2=∑i,j=1NwiwjCov(Ri,Rj)\sigma_P^2 = \sum_{i,j = 1}^N w_i w_j Cov(R_i, R_j)

σP2=∑i=1Nwi2Var(Ri)+∑i,j=1,i≠jNwiwjCov(Ri,Rj)\sigma_P^2 = \sum_{i=1}^N w_i^2 Var(R_i) + \sum_{i,j = 1, i \neq j}^N w_i w_j Cov(R_i, R_j)

where $Cov(Ri, R_j) = \rho{ij} \sigmai \sigma_j = \frac{\sum{t=1}^N \lbrace [R{t,i} - \bar{R_i}] [R{t,j} - \bar{R_j}]\rbrace}{N}$

other investment characteristics

  • skewness

    • skewness of normal distribution is 0

    • skewed to the Right (Positively Skewed)

    • skewed to the Left (Negatively Skewed)

  • kurtosis (峰度)

    • kurtosis of normal distribution is 3

    • kurtosis > 3 refers to flat, fat tail

    • kurtosis < 3 refers to thin peak

risk aversion and portfolio selection

risk aversion: the degree of an investor's inability and unwillingness to take risk

  • risk seeking:

  • risk neutral: if an investor is indifferent about the gamble or the guaranteed outcome, then the investor may be risk neutral.

  • risk averse: the assumption that an investor will choose the least risky alternative

risk tolerance

risk tolerance refers to the amount of risk an investor is willing to tolerate to achieve an investment goal.

utility theory

  • utility function: U=E(r)−12Aσ2U = E(r) - \frac{1}{2} A \sigma^2 where, U is the utility of an investment, E(r) is the expected return, and $sigma^2$ is the variance of the investment, A is a measure of risk aversion, A is higher for more risk-averse individual.

  • indifference curve: representing all the combinations of two goods or attributes such that the consumer is entirely indifferent among them.

application of the utility theory

The equation for the capital allocation line is shown as follows: E(Rp)=(1−σpσi)Rf+σpσiE(Ri)E(R_p) = (1 - \frac{\sigma_p}{\sigma_i}) R_f + \frac{\sigma_p}{\sigma_i} E(R_i)

This equation can be rewritten in a more usable form:

E(Rp)=Rf+E(Ri)−Rfσi)σpE(R_p) = R_f + \frac{E(R_i) - R_f}{\sigma_i}) \sigma_p

minimum-variance portfolios

Capital Allocation Line (CAL) and Optimal Risky Portfolio

CAL is the combination of the risk-free asset with zero risk and the portfolio of all risky assets

Optimal Investor Portfolio

capital market theory

capital market line (CML)

market: a means of bringing buyers and sellers together to exchange goods and services

The portfolio return and portfolio standard deviation can be simplified and rewritten as: E(Rp)=Rf+(E(Rm)−Rfσm)×sigmapE(R_p) = R_f + (\frac{E(R_m) - R_f}{\sigma_m}) \times sigma_p

Investors who believe market prices are informationally efficient often follow a passive investment strategy.

pricing of risk and computation of expected return

systemic risk and non-systematic risk

  • systematic risk: risk that affects the entire market or economy; it cannot be avoided and is inherent in the overall market. Systematic risk is also known as non-diversifiable or market risk.

  • non-systematic risk: unique risk that is local or limited to a particular asset or industry that need not affect assets outside of that asset class.

e.g.

  • a risk-free asset has no risk. Therefore, a risk-free asset has zero systematic risk and zero non-systematic risk.

Total variance = systematic variance + non-systematic variance

return-generating models

a return-generating model is a model that can provide an estimate of the expected return of a security given certain parameters and estimates of the values of the independent variable in the model.

multi-factor model is a model that explains a variable in terms of the values of a set of factor

A general return-generating model is expressed in the following manner: E(Ri)−Rf=∑j=1kβijE(Fj)=βi1[E(Rm)+Rf]+∑j=2kβijE(Fj)E(R_i) - R_f = \sum_{j=1}^k \beta_{ij} E(F_j) = \beta_{i1} [E(R_m) + R_f] + \sum_{j=2}^k \beta_{ij} E(F_j)

The model has k factors, the coefficients $\beta_{ij}$ are called factor weights or factor loadings associated with each factor.

decomposition of total risk for a single-index model

E(Ri)−Rf=βi[E(Rm)−Rf]E(R_i) - R_f = \beta_i [E(R_m) - R_f] and $R_i - R_f = \beta_i (R_m - R_f) + e_i$

Where, $e_i$ is an error term. The total variance can be decomposed into systematic and non-systematic variances in the second equation below: σi2=βi2σm2+σe2+2Cov(Rm,ei)\sigma_i^2 = \beta_i^2 \sigma_m^2 + \sigma_e^2 + 2 Cov(R_m, e_i)

Total variance = systematic variance + non-systematic variance, which can be written as

σi=βi2σm2+σe2\sigma_i = \sqrt{\beta_i^2 \sigma_m^2 + \sigma_e^2}

Because non-systematic risk is zero for well-diversified portfolio and systematic risk can be seen as $\beta_i \sigma_m$. So

E(Ri)−Rf=βi[E(Rm)−Rf]E(R_i) - R_f = \beta_i [E(R_m) - R_f] and

βi=Cov(Ri,Rm)σm2=ρi,mσiσmσm2=ρi,mσiσm\beta_i = \frac{Cov(R_i, R_m)}{\sigma_m^2} = \frac{\rho_{i,m} \sigma_i \sigma_m}{\sigma_m^2} = \frac{\rho_{i,m} \sigma_i}{\sigma_m}

Beta is a measure of the sensitivity of a given investment or portfolio to movements in the overall market.

the capital asset pricing model

the assumption of the CAPM are:

  • investors are risk-averse, utility-maximizing, rational individuals

  • markets are frictionless, including no transaction costs and no taxes

  • investors plan for the same single holding period

  • investors have homogeneous expectations or beliefs

  • all investments are infinite divisible

  • investor are price takers

the security market line

The security market line (SML) is a graphical representation of the capital asset pricing model with beta, reflecting systematic risk $\beta$, on the x-axis and expected return $R_m$ on the y-axis.

portfolio beta

βp=∑i=1nwiβi; ∑i=1nwi=1\beta_p = \sum_{i=1}^n w_i \beta_i;\ \sum_{i=1}^n w_i = 1

The portfolio's return given by the CAPM is

E(Rp)−Rf=βp[E(Rm)−Rf]E(R_p) - R_f = \beta_p [E(R_m) - R_f]

portfolio performance evaluation

  • sharpe ratios: the average return in excess of the risk-free rate divided by the standard deviation of return; a measure of the average excess return earned per unit of standard deviation of return Sharpe ratio=Rp−RfσpSharpe\ ratio = \frac{R_p - R_f}{\sigma_p}

  • Treynor ratio: a measure of risk-adjusted performance that relates a portfolio's excess returns to the portfolio's beta Treynor ratio=Rp−RfβpTreynor\ ratio = \frac{R_p - R_f}{\beta_p}

  • M-squared ($M_2$) M2=(Rp−Rf)σmσp−(Rm−Rf)M_2 = (R_p - R_f) \frac{\sigma_m}{\sigma_p} - (R_m - R_f)

  • Jensen's alpha αp=Rp−[Rf+βp(Rm−Rf)]\alpha_p = R_p - [R_f + \beta_p (R_m - R_f)]

beyond the CAPM

limitations of the CAPM

  • Theoretical limitations of the CAPM

    • single-factor model: only systematic risk or beta risk is priced in the CAPM.

    • single-period model: the CAPM is a single-period model that does not consider multi-period implications or investment objectives of future periods, which can lead to myopic and suboptimal investment decisions.

  • practical limitation of the CAPM

    • market portfolio

    • proxy for a market portfolio: use proxies instead of a true market portfolio

    • estimation of beta risk

    • the CAPM is a poor predicator of returns

    • homogeneity in investor expectations: the CAPM assumes that homogeneity exists in investor expectations which do not actually happen.

miscellaneous

  • an investor's optimal portfolio is the combination of a risk-free asset and a risky asset with the highest indifference curve.

  • the market portfolio consists of all risky assets

  • only systematic risk is priced in CAPM

  • use beta to measure the market risk

  • M-squared adjusts for risk using standard deviation

  • if expected return of an asset is higher than CAPM price, the asset is undervalued

basic of portfolio planning and construction

investment policy statement (IPS) will typically begin with the investor's goals in terms of risk and return. The IPS provides the client's needs, circumstances, and constraints for better investment. Having a written IPS is part of best practice for a portfolio manager; the IPS may be required by regulation

major components of an IPS

  • introduction

  • statement of purpose

  • statement of duties and responsibilities

  • procedures

  • investment objectives

  • investment constraints

  • investment guidelines

  • evaluation and review

  • appendices:(A) strategic asset allocation (B) rebalancing policy. Many investors specify a strategic asset allocation (SAA).

risk objectives

  • absolute risk objective

  • relative risk objective relate to a specific benchmark

return objectives

similar to risk objectives, return objectives may be stated on an absolute or a relative basis.

  • ability to bear risk

  • willingness to bear risk

investment constraints

Memory point: R-R-T-T-L-L-U

Objective

  • Risk

  • Return

Constraints

  • Time horizon

  • Tax situation

  • Liquidity

  • Legal restrictions

  • Unique constraints of a specific investor

After having determined the investor objectives and constraints through the exercise of creating an IPS, a strategic asset allocation is developed which specifies the percentage allocations to the included asset classes

portfolio construction

  • capital market expectations are the investor's expectations concerning the risk and return prospects of asset classes, however broadly or narrowly the investor defines those asset classes.

  • tactical asset allocation: is the decision to deliberately deviate from the strategic asset allocation in an attempt to add value based on forecasts of the near-term relative performance of asset classes.

  • security selection: the process of selecting individual securities; typically, security selection has the objective of generating superior risk-adjusted returns relative to a portfolio's benchmark.

  • a strategic asset allocation results from combining the constraints and objectives articulated in the IPS and capital market expectations regarding the asset classes.

  • As time goes on, a client's asset allocation will drift from the target allocation, and the amount of allowable drift as well as a rebalancing policy should be formalized.

  • In addition to taking systematic risk, an investment committee may choose to take tactical asset allocation risk or security selection risk. The amount of return attributable to these decisions can be measured.

miscellaneous

  • property and casualty insures have greater liquidity needs than life insurance companies

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