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CFA-Equity
A super detailed mind map of the first-level rights test points is here! It summarizes the key knowledge of two major categories: financial system and securities market. You can supplement your knowledge points by doing the questions. I wish you an easy landing!
Edited at 2021-07-04 17:17:53- bacteria
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CFA-Equity
- bacteria
This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
- Plant asexual reproduction
This is a mind map about plant asexual reproduction, and its main contents include: concept, spore reproduction, vegetative reproduction, tissue culture, and buds. The summary is comprehensive and meticulous, suitable as review materials.
- Reproductive development of animals
This is a mind map about the reproductive development of animals, and its main contents include: insects, frogs, birds, sexual reproduction, and asexual reproduction. The summary is comprehensive and meticulous, suitable as review materials.
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- Outline
Equity Equity
securities market
organization and structure
Financial system
financial system functions
1. Achieving entities purposes in using financial system
1. Saving
2·Borrowing
3·Raising equity capital Raising equity capital
4·Managing risks Risk management
5·Exchanging assetsExchanging assets
6·Information-motivated trading Information-motivated trading
2. Determining equilibrium rates of return Determining equilibrium rates of return
Determined by market supply and demand
3. Capital allocation efficiency Capital allocation efficiency (asset allocation)
Market Assessment and Regulation
The objectives of market regulation The objectives of market regulation
Control fraud
Control agency problems Control agency problems
Promote fairness Promote social fairness
Set mutually beneficial standards Set mutually beneficial standards
Prevent undercapitalized financial firms from exploiting their investors by making excessively risky investments Prevent undercapitalized financial firms from exploiting their investors by making excessively risky investments
Ensure that long-term liabilities are funded Ensure that long-term liabilities are funded
Characteristics of a well-functioning financial system
Complete markets Market integrity
Operational efficient
Market liquidity is good enough and transaction costs are low enough
Informationally efficient Informationally efficient
Allocationally efficient aseman Resource allocation is efficient
financial intermediary
Brokers
earn commission
Block brokers
Dealers Market Makers
Participate in market transactions and earn the difference
Brokers, market makers have conflicts of interest over how they fill their customers' orders
Investment banks Investment banks
Securitizers
Alternative trading systems (ATS) alternative trading systems (similar to exchanges, less supervision)
Market classification
Classification of each dimension
Based on delivery date
Spot markets vs Futures markets Spot markets vs Futures markets
Based on time maturity based on expiration time
Money markets vs Capital markets Money markets vs Capital markets
Based on position and underlying Based on position and underlying asset
Traditional markets vs, Alternative markets Traditional markets vs, Alternative markets
Arbitrageurs Clearingnouses clearinghouse Custodians Exchanges Exchanges Depository institutions Insurance companies Depository institutions Insurance companies
Based on capital flow Based on capital flow
Primary markets Vs Secondary markets Primary markets and secondary markets
primary market
Public offering Public offering
IPO (initial public offerings) initial public offering
Underwritten offering underwriting
Greater risk for brokers
Best effort offering consignment
Greater risk for listed companies
Under the same conditions, under which model will brokerage commissions be higher? If the bond bears higher risk, the commission fee required by it will be higher (underwriting issuance cost > agency issuance cost)
Seasoned offerings(secondary issues) additional issuance
private placement (private placement/private placement)
For qualified investors
Shelf registration(advance registration/suspension registration)
Dividend reinvestment plans (DRPs) dividend reinvestment
right offering(equity sale)
Secondary market
Classified by trading session Classified by trading session
Call market (collective bidding market)
Continuous market
Compared
Classified by trading mechanism Classified by trading mechanism
Quote-driven markets
Brokered markets
Order-driven markets
Order matching rules two sets of rules
1. Order matching rules Order matching rules
Price priority Price priority
Display precedence Display priority
Time precedence time priority
2. Trading Pricing rules Trading pricing rules
Uniform pricing rule Single pricing rule
Discriminatory pricing rule discriminatory pricing rule
Derivative pricing rule Derivative pricing rule
Asset Classification
Financial assets Financial assets
Based on underlying characteristic
Securities Securities
Fixed-income: bonds, repos, CDs Fixed-income: bonds, repos, certificates of deposit
Equity: common/preferred shares Equity: common shares and preferred shares
Pooled investment vehicles close/open-ended fund, ETFs Pooled investment vehicles closed/open-ended fund, ETFs
Derivative contracts Derivative contracts
Based on whether trade publicly Based on whether trade publicly
Public securities
Private securities
Physical assets physical assets
Commodities: industrial metals, agricultural products Commodities: industrial metals, agricultural products
Real assets: real estate airplanes, machinery Real assets: real estate airplanes, machinery
Currencies Currencies
position
basic concept
Short selling
Short selling
Investor borrows stock and sells it Investors borrow stock and sell it
Repurchases the stock and returns it to the lender (covers the short position) Repurchases the stock and returns it to the lender (covers the short position)
Payments-in-lieu
Short rebate rate
Leveraged financing
Buy on margin
margin loan/borrowed fund: A borrowed loan is called a margin loan/borrowed fund
The interest rate that the buyers pay for margin loan is the call money rate (financing cost rate) The interest rate that the buyers pay for margin loan is the call money rate
Buyer's equity is the portion of the security price that belongs to the buyer
Financial leverage ratio Financial leverage ratio
Initial margin requirement Initial margin requirement
Maintenance margin requirement Maintenance margin requirement
Margin call margin call
instruction
quotation
Prices quoted by dealers (market makers) Prices quoted by dealers (market makers)
Bid price purchase price
Ask/offer price selling price
Bid-ask spread Bid-ask spread
Instructions attached to orders Instructions attached to orders
Execution instructions Execution instructions
Validity instructions Validity instructions
Clearing instructions Clearing instructions
Execution orders
Market orders Market orders: Instruct the broker to buy or sell immediately at the current best price
Advantages: fast
Disadvantages: Transaction price is uncertain
Limit orders limit orders: Instruct the broker to buy or sell immediately at the current best price
Advantages: The transaction price is determined
Disadvantages: may not be fully completed
Marketable limit orders
proper noun
Make the market
Participate in market making
Make a new market
Make a new market
Behind the market
Far from the market
All-or-nothing orders
Either all transactions or none
Hidden orders
Iceberg orders
Validity Instructions
Day orders (valid orders on the day)
Expires if not filled by end of trading day
Good-till-cancelled
Valid until transaction is completed
Immediate-or-cancel(Fill-or-kill)
The untransacted portion will be invalidated.
Good-on-close orders
Match the closing time point with the closing market situation
Good-on-open orders
Match the opening time point with the opening market situation
Stop orders
It cannot be filled until the stop price condition is met.
stop sell order
Holders are worried that the stock will fall, long
stop buy order
Holders are worried that the stock will rise, short
market index
Basic concepts of indices
lndex construction steps index construction steps
1. Which target market should the index represent? Which target market should the index represent?
subtopic
2. Which securities should be selected from that target market? Which securities should be selected from the target market?
3. How much weight should be allocated to each security in the index? How much weight should be allocated to each security in the index?
4. When should the index be rebalanced? When should the index be rebalanced?
5. When should the security selection and weighting decision be re-examined? When should the security selection and weighting decision be re-examined?
Index value and return calculation
Price return index &Total return index
What is the index used for?
1. Gauges of market sentiment Measurement of market sentiment 2. Proxies for measuring and modeling returns, systematic risk, and risk-adjusted performance A proxy for measuring and modeling returns, systematic risk and risk-adjusted performance 3. Proxies for asset classes in asset allocation models Proxies for asset classes in asset allocation models 4. Benchmarks for actively managed portfolios Benchmarks for Actively Managed Portfolios 5. Model portfolios for such investment products as index funds and ETFS (exchange-traded funds.) Build portfolio models for investment products such as index funds and ETFs
Various market indices
Equity index
Broad market indices represent an entire equity market Broad market indices represent an entire equity market
Multi-market indices comprise indices from different countries
Sector indices represent different economic sectors Sector indices represent economic sectors that are not
Style indices represent securities classified according to market capitalization,value, growth,etc Style indices represent securities classified according to market capitalization, value, growth, etc.
Fixed-income index
Broad universe: fixed-income securities can be classified along many dimensions Broad universe: fixed-income securities can be classified along many dimensions
High turnover due to securities mature Due to the maturity of securities, the turnover rate is high
Stocks have no expiration date and low turnover rate
Dealer markets and illiquidity Dealer markets and illiquidity
real estate index
Categorized as appraisal indices, repeat sales indices, and REITS indices Real estate indices are divided into appraisal indices, repeat sales indices, and REITS indices
Commodity indices
the performance of commodity indices may be quite different from their underlying commodities
Hedge fund index hedge fund index
Index providers rely on the voluntary cooperation of hedge funds Index providers rely on the voluntary cooperation of hedge funds
May have survivorship bias
How the index is constructed
Price weighting Price weighting
algorithm
The index value is the arithmetic average of security prices Index value is the arithmetic mean of security prices
It's simply done by buying an equal number of shares of each security in the index Buy the same number of shares for each stock
Advantage: simplicity Advantages: Simple
Disadvantage: ·Highly priced securities have a greater influence on index value Highly priced securities have a greater impact on the index value ·When a stock-split occurs, the divisor is adjusted so that the index value is maintained unchanged When a stock split occurs, the divisor is adjusted so that the index value remains the same
Market-capitalization weighting Market-capitalization weighting
Market-capitalization weighting
The weight is determined by dividing a stocks market capitalization by the total market capitalization of the index The weight is determined by dividing a stocks market capitalization by the total market capitalization of the index
Advantage:
constituent stock's weight equals to its actual market fraction
Stock splits will not affect market capitalization weighting
Disadvantage: firms with larger market capitalizations have a greater nfluence on the indexes value which leads to momentum tilt Companies with larger market capitalization have a greater nfluence on the indexes value which leads to momentum tilt
Float-adjusted market-cap weighting Float-adjusted market-cap weighting
Excluding restricted shares, stocks held by controlling shareholders
The weight is determined by adjusting its market capitalization for its market float, which is the number of shares available to the investing public number of shares
Free-float-adjusted market capitalization weighting Free circulation for weighted average
Then remove stocks that are not available to foreign investors.
Further reduce the number of shares by excluding shares not available to foreign investors Further reduce the number of shares by excluding shares not available to foreign investors
Equal weighting Equal weighting
Each constituent security has an equal weight, and the index return is the arithmetic mean of HPRs on index stocks
The index is matched by investing equal dollar amount in each stock
algorithm
Advantage
simplicity
Disadvantage
1. Small-cap bias: small-cap stocks are over-presented, because it is over-weighted and has greater volatility, so the index will fluctuate sex
2. Requiring frequent rebalance as prices change. Need to do rebalancing frequently.
3. In theory, it can be compiled, but in reality it is impossible to buy it.
Fundamentally weighting Fundamentally weighting
This method uses measures of a company's size that are independent of its security price to determine the weight on each constituent security
These measures include book value, cashflow, revenues, earnings, dividends, and number of employees
It leads to indexes that have a "value" tilt
It leads to indexes that have a contrarian effect
Value tilt, generally we construct an index weighted by price or market value. When market speculation prevails, the price will often deviate significantly from the basic value. The greater the price increase, the more the market value increases, and the proportion in the index will be The larger the index, the more overvalued stocks will be purchased if the index is used as a reference to build a portfolio. Therefore, in order to correct this flaw, there is an index constructed based on basic financial indicators. At this time, when constructing a portfolio using this index, stocks whose relative value has declined, that is, stocks that are undervalued, are often selected and given a larger value. The weight of stocks with relatively high relative value will be given smaller weights. Because it is contrary to common sense, it is called the "reverse effect", also called "value tilt".
summary
Index rebalancing and rebuilding
Rebalancing
Price-weighted indexes are not rebalanced Price-weighted indexes do not need to be rebalanced
For market-capitalization-weighted indexes, rebalancing is less of a concern, because the indexes largely rebalance themselves
They are only adjusted to reflect mergers,acquisitions, liquidations, etc.
Equal-weighted indexes requires most frequent rebalancing Equal-weighted indexes require most frequent rebalancing
Reconstitution
Constituent securities that no longer meet the criteria are replaced with securities that meet the criteria Constituent securities that no longer meet the criteria are replaced with securities that meet the criteria
Reconstitution is part of the rebalancing cycle Reconstitution is part of the rebalancing cycle
market efficiency
efficient market theory
Related concepts of market efficiency
Informationally efficient market: a market in which asset prices reflect new information quickly and rationally Information efficient market: a market in which asset prices reflect new information quickly and rationally
Passive investment strategy is preferred to active strategy due to lower costs Passive investing strategies are better than active investing strategies due to lower costs
Follow passive investing
Prices react only to the "unexpected"information Prices only react to "unexpected" information
in an efficient market, market prices accurately reflect intrinsic values In an efficient market, market prices accurately reflect intrinsic values
Factors that affect market efficiency Factors that affect market efficiency
Number of market participants Number of market participants
Information availability Information availability
Limits to trading will impede market efficiency Limits to trading will impede market efficiency
Transaction costs and information acquisition costs Transaction costs and information acquisition costs
Roles for portfolio manager in efficient marke Roles for portfolio managers in efficient market
Establish portfolio risk/ return objectives Establish portfolio risk/return objectives
Implement asset allocation based on risk/ return objectives
Portfolio diversification diversification
Tax minimization tax burden minimization
efficient market hypothesis
Weak-form efficient market hypothesis weak efficient market
Extra returns can be obtained through fundamental analysis and insider trading
Technical analysis is invalid
Securities prices reflect all historical prices and trading volumes information Securities prices reflect all historical prices and trading volumes
Investors can not consistently earn abnormal profits using technical analysis Investors can not consistently earn abnormal profits using technical analysis
Semi-strong form efficient market Semi-strong form efficient market
Fundamental analysis is invalid
Use inside information to obtain excess returns
Securities prices accurately and quickly reflect all public information Securities prices accurately and quickly reflect all public information
Investors can not consistently earn abnormal profits using fundamental analysis Investors can not consistently earn abnormal profits using fundamental analysis
The semi-strong form encompasses the weak-form
Strong-Form efficient market hypothesis Strong-Form efficient market
Insider information is invalid
Securities prices fully reflect both public and private information Securities prices fully reflect both public and private information
Insiders can't consistently earn abnormal returns from trading on private information Insiders can't consistently earn abnormal returns from trading on private information
Strong form encompasses semi-strong and weak form Strong form encompasses semi-strong and weak form
Market anomalies Market anomalies
In the wide-spread search for discovering profitable anomalies, many findings could simply be the product of a process called data mining (data snooping) data snooping) process
1. Time-series anomalies
Calendar anomaly calendar effect
January effect / turn-of-the-year effect January effect
window dressing window dressing
tax-loss selling tax-loss selling
Turn-of-the-month effect Turn-of-the-month effect
Day-of-the-week effect
Weekend effect
Holiday effect
Momentum and overreaction anomalies
Momentum inertia effect
Chasing the rise and killing the fall (contrary to market efficiency)
Overreaction effect Overreaction effect
2. Cross-sectional anomalies
Size effect
Value effect Value effect
3. Other anomalies
Closed-end fund discounts Closed-end fund discounts
Earnings surprise Earnings surprise
Initial public offerings (IPOs) Initial Public Offering (IPO)
Behavioral Finance
The behavior of individuals, particularly their behavioral biases, is considered a possible explanation for many pricing anomalies
Market efficiency and asset pricing models do not require that every individual be rational – rather, only that the market is rational
Loss aversion loss aversion
Representative bias Selective bias
Overconfidence Overconfidence
Mental accounting Mental accounting
Conservatism
Narrow framing representation bias
Herding effect herding effect
information cascade information waterfall
It may be rational, but if it is developed to the extreme, it will become a herd effect and become irrational behavior.
equity investment
Equity Securities Overview
Types of equity assets
Common shares Common shares
Have a residual claim on company's net assets in liquidation Have a residual claim on company's net assets in liquidation
The payments of dividend are not contractually obligation The payments of dividend are not contractually obligation
You can choose to issue or not to issue, the decision lies with the listed company.
Participate in the governance process through voting rights Participate in the governance process through voting rights
Statutory voting statutory voting rights
Disadvantages: The controlling shareholder has an advantage in the number of shares and controls the final election results, while small shareholders are disadvantaged.
cumulative voting cumulative voting
The number of shares in hand × the number of seats selected, small and medium shareholders gather their strength to do big things
Proxy voting proxy voting
Companies can issue different classes of common shares, with each class offering different ownership rights Companies can issue different classes of common shares, with each class offering different ownership rights
Same shares have different rights, concentrating power in the hands of a few people
Callable common shares & putable common shares Callable common shares & putable common shares
preferred stock
Preference shares Preference shares
Similar to debt securities Similar to debt securities
The dividends are fixed The dividends are fixed
Do not have voting rights Do not have voting rights
Do not share in the operating performance of the company Do not share the operating performance of the company
Similar to common shares Similar to common shares
Preference shares can be perpetual
Dividends are not contracta obligations Dividends are not contracta obligations
Can be callable or putable
Cumulative preference shares Cumulative preference shares
No dividend will be paid this year, but will be paid cumulatively next year
Participating preference shares Participating preference shares in management
Preferred stock dividends have been distributed, and when it is the turn of common shares to be distributed, preferred stocks will also get a share of the dividends.
Convertible preference shares Convertible preference shares
private equity securities
Types of private securities investment Types of private securities investment
Venture capital investments Venture capital
Leveraged buyout (LBO) Leveraged buyout
Private investment in public equity (PIPE) private equity investment
Characteristic of private securities Characteristics of private securities
No active secondary markets No active secondary markets
Potentially greater return Potentially greater return
Less transparent than public securities Less transparent than public securities
Lower reporting costs reporting costs lowering
Greater ability to focus on long-term prospects because there is no public pressure for short-term results Greater ability to focus on long-term prospects because there is no public pressure for short-term results
depository receipts
Sponsored DR Participating Depositary Receipt
Investors: voting rights, dividend rights
Unsponsored DR non-participating depositary receipt
Investors only have the right to dividends
Bank: voting rights
American depository receipts (ADRs)
USD denominated
Global depositary receipts (GDRs)
Denominated in other than U.S. dollars
There is exchange rate risk
Risk and return characteristics of equity securities
Risk of equity securities Risk of equity securities
Preference shares are less risky than common shares Preference shares are less risky than common shares
Putable shares are less risky than callable or non-callable shares Putable shares are less risky than callable or non-callable shares
For investors: Putable risk < non callable/Putable risk < callable risk
对于发行者：Putable risk > non callable/Putable risk> callable risk
站在发行公司的角度， 可卖回优先股(puttable)的风险是最高的，因为投资者可以以约定好的价格把股票卖回给发行公司。 可赎回优先股(callable preference shares)的风险最低，因为公司可以以一个约定好的价格买回投资人持股。 Non-callable优先股风险介于puttable和callable之间。
Cumulative / participating preference shares are less risky than non-cumulative / non-participating preference shares Cumulative / participating preference shares are less risky than non-cumulative / non-participating preference shares
Cumulative risk < non-cumulative risk
participating risk < non-participating risk
Return on equity (ROE)
Cost of equity
industry analysis
Category
Approach to identify similar companies
1. Product or services supplied
2. Business-cycle sensitivities Business cycle sensitivities
Test points
Cyclical company
Non-cyclical company Non-cyclical company
Defensive company defensive company
growth company growth company
Limitations
• Severe recessions may affect all companies A severe economic downturn could affect all companies
• Different regions may experience different stages Different regions may go through different stages
3. Statistical similarities. Statistical similarities.
Limitations
Often result in non-intuitive groups of companies (the economic substance is not taken into account, the result has no logical reason)
The composition may vary by time and region The composition may vary by time and region (statistical patterns will change and may change frequently)
No guarantee that past correlations will continue in the future
Carry the inherent dangers of all statistical methods Carry the inherent dangers of all statistical methods (defects in statistics will be encountered)
Peer group
Strategic Analysis
Porter's Five Forces Analysis
Porters five forces model
The intensity of industry competition depends on
1. Rivalry among existing competitors Rivalry among existing competitors
2. Threat of new entrants Threat of new entrants
3. Threat of substitute products Threat of substitute products
4. Bargaining power of buyers Bargaining power of buyers
Downstream power
5. Bargaining power of suppliers Bargaining power of suppliers
Upstream power
Factors affecting pricing power
Barriers to entry Barriers to entry
Market share stability Stable market share
unstable market shares unstable market share, limited pricing power, the lower the pricing power
In a stable market, leading companies will occupy a larger market share.
Stable market with high barriers to entry and low competition
In a stable market, customers’ switching costs for sub-commodities tend to be higher.
Industry concentration Industry concentration
Relative market share has greater impact
Industry capacity Industry capacity
Industry life cycle Industry life cycle
Company competitive strategy analysis
1. Cost leadership (low cost) Cost leadership (low cost)
Lowest costs of production, lowest prices Lowest costs of production, lowest prices
Sell enough volume to earn superior return Sell enough volume to earn superior return
2. Product or service differentiation Product or service differentiation
Distinctive in terms of type, features, quality, or delivery Distinctive in terms of type, features, quality, or delivery
Achieve price premium Achieve price premium
3. Focus
Equity estimate
discounted cash flow model
Dividend related concepts
Cash dividend
regular cash dividend
Special / extra dividends Special / extra dividends
Stock dividend
Does not change total shareholder wealth
Stock split & reverse stock split
Share repurchase Share repurchase
Cash payment dividend chronology
dividend discount model
Gordon Growth Model
Assumptions
The dividend growth rate is forever and never change
The required rate of return is constant overtime The required rate of return is constant in the long run
The dividend growth rate is less than the required rate of return The dividend growth rate is less than the required rate of return
Two-stage DDM models Two-stage DDM models
Suppose the company goes through an initial limited period of high growth, followed by an unlimited period of sustained growth.
Applicable to companies that have gone through the growth stage and are currently in the transition stage and are about to transition to the maturity stage
three-stage dividend discount model three-stage model
The three-stage dividend discount model is usually suitable for the valuation of young, growth-stage companies.
Preferred stock valuation
D=par value × fixed rate
multiplier model
price multiplier model
Price multiple
Price multiples based on fundamentals: the stock value is justified by fundamentals or a discount cash flow model
The relationship between P/E and payout ratio is ambiguous, because a higher payout ratio may imply as lower growth rate The relationship between P/E and payout ratio is ambiguous, because a higher payout ratio may imply as lower growth rate Rate
advantage
Allow for relative comparisons, both cross-sectional and in time-series Allow for relative comparisons, including horizontal comparisons and time-series comparisons
Price multiples are popular among investors Price multiples are popular among investors
shortcoming
May generate a contradictory conclusion with those of the discounted cashflow methods May generate a contradictory conclusion with those of the discounted cashflow methods
Differences in accounting standards and/or methods can result in multiples not easily comparable Differences in accounting standards/or methods can result in multiples not easily comparable
The multiples for cyclical companies maybe highly influenced by current economic conditions The multiples for cyclical companies maybe highly influenced by current economic conditions
Enterprise Value Multiplier Model
Enterprise value is often viewed as the cost of a takeover
Enterprise value is most useful when comparing companies with significant differences in capital structure Enterprise value is most useful when comparing companies with significant differences in capital structure
Asset-Based Valuation Model
Market value of equity=
market value of assets - market value of liabilities
Appropriate appropriate
Primarily tangible short-term assets Primarily tangible short-term assets
Assets with ready market values Assets with ready market values
Firms are held privately Firms are held privately
Firms cease to operate and are being liquidated Companies cease to operate and are being liquidated
Inappropriate
Assets that do not have easily determinable market values Assets that do not have easily determinable market values
Fair values of assets and liabilities can be very different from their book values Fair values of assets and liabilities can be very different from their book values
It may understate company value with a floor"value
Hyper-inflationary environment It is difficult to estimate if hyperinflation occurs
rights offering rights offering: private offering, only to existing shareholders price placement private placement: private offering, to new investors
IPO: 1. Initial public offering 2. Open to the public (available to everyone)
bond index providers rely on dealers for prices. Since most bonds do not have a public market price, index builders often rely on quotes from market makers to value bonds.
Weak efficient market: Technical analysis can temporarily gain gains Fundamental analysis can lead to sustained excess returns Technical analysis, you can get normal/average returns
Equity value, return and cost
puttable bond: Puttable bond: gives the bondholder the right to sell the bond back to the issuer at a predetermined price on a specific date
callable bond: A callable bond gives the issuer the right to redeem all or part of the bond before a specified maturity date
If the price of the hidden order is better than that of the displayed order, then the hidden order will be executed directly at this time (price priority > display priority)
The P/E ratio is inversely related to the required rate of return, and positively related to the growth rate The P/E ratio is inversely related to the required rate of return, and positively related to the growth rate