Types of Exchange Rate Risk

1. Transaction Exposure - I am a US investor expecting to receive 1m Euro in 2 years from a client. I don't know what the euro will be worth in 2 years.

Transaction exposure can be mitigated using derivatives. I can short a 2-year USD/EUR forward to mitigate the risk



2. Translation Exposure - this is associated with accounting when on the financial statements one currency is converted to another without necessarily any real economic gains or losses.


3. Economic Exposure - when changes in the currency rates affect the competitive standing of the business. A Russian consumer products manufacturer (with expenses and revenues in Rubles) is likely to sell more products to foreign clients if the local Russian currency devalues

Wealth Management Concepts

Goals Based Planning Financial Planning - modifies traditional MVO and accommodates for behavioral finance. The financial asset portfolio is dividend into risk buckets:

1. Personal Risk - cash, money market funds, personal residence is included

2. Market Risk - fixed income and equity market portfolio

3. Aspirational - concentrated positions etc

Primary Capital = Personal Risk Bucket + Market Risk Bucket

Surplus Capital = Aspirational Risk Bucket


Estate Planning Concepts:

Human Capital = Net Employment Capital = Present Value of Income Generated Over Lifetime

Core Capital = Amount of assets needed to meet all the individual's liabilities + reserve for unexpected needs

Excess Capital = Total Assets (financial + human capital) - Total Liabilities (financial and non-financial)

We can use mortality table or monte carlo simulation to estimate core capital

Notice that if a man with all the same characteristics as a woman but who is likely to live less, his core capital is likely to be less

Individual Risk Management Concepts

A risk with the loss characteristics of high frequency of occurrence and low severity of loss, such as dental cavities, is best managed through risk reduction—for example, through proper dental hygiene. A risk with the loss characteristics of low frequency of occurrence and high severity of loss, such as an earthquake that destroys your home, is best managed through risk transfer. A risk with the loss characteristics of low frequency of occurrence and low severity of loss is best managed through risk retention, such as not purchasing an extended warranty on an infrequently used and relatively inexpensive item.

GIPS Need to Know List

REQUIRED Disclosures

1. Definition of the Firm
2. Total assets under management (all types)
3. Composite description and creation date
4. Benchmark description
5. Currency used
6. if gross of fees returns are presented must disclose any deductions other than direct trading expenses. 
7. for net of fees returns must: a) disclose any deductions other than trading expenses and investment management fees b) if actual or model investment management fees are used and c) if returns are net of performance based fees 
8. State that composite descriptions are available upon request
9. Disclose valuation & performance measurement policies upon request
10. Disclose presence of leverage, short positions and use of derivatives. 
11. Significant events that would help interpret performance e.g. departure of key investment managers
12. For any non-compliant performance betfore 2000, must disclose period of non-compliance
13. If the firm or composite is redefined, must disclose date, description and reason
14. Must disclose minimum asset level 
15. Must disclose if the name of the composite was changed. 
16. Must disclose relevant treatment of taxes if material and provide benchmark returns net of withholding taxes if available
17. From 1st of Jan 2011, Must disclose any material differences in valuation sources and exchange rates used. (e.g. i used reuters for valuation in one portfolio and Bloomberg in another)
18. Must disclose any conflicts between GIPS and local laws/regulations
19. Must disclose carve out cash policies prior to 1 Jan 2010 (after carve outs were no longer allowed)
20. Must disclose fees included in the bundled fee
21. Disclose any sub advisors and periods they were used from jan 1 2006
22. For periods prior to 2010, must disclose if portfolios were not valued at calendar month end or last business day
23. After 2011, must disclose any material subjective unobservable inputs employed for valuation purposes and any difference in the valuation hierarchy than the one recommended
24. If no benchmark exists, must disclose why
25. If benchmark is changed must disclose date & reason
26. For custom benchmark, must disclose details of the benchmark including components, weights and rebalancing process
27. If the firm has a significant cash flow policy, must disclose how the firm defines it
28. Must disclose if a 3-year annualized ex-post standard deviation for the composite or benchmark is not presented because returns are not available
29. If the firm decides that the 3-year standard deviation is to be excluded because it is not relevant, must disclose why it is not relevant and a description of the alternative risk measure used with reason for its use
30. Must disclose if performance from past firm or affiliation is linked to the performance of the firm

Note valuation hierarchy:

1. Objective unadjusted market prices for similar investments in active markets

2.  Quoted prices for similar investments in non active markets

3. Use market based inputs other than prices

4. Subjective unobservable inputs

RECOMMENDED Disclosures

1. Disclose any material changes to valuation or calculation policies

2. Disclose material differences between the benchmark and the composite's investment mandate, objective or strategy

3. Key assumptions used to value portfolio investments

4. List of other firms contained within the parent company (if relevant)

5. Disclose any subjective unobservable inputs used to value portfolios prior to 2011 (after 2011 mandatory to disclose)

6. Disclose sub advisor used for periods prior to 2006

Investment Policy Statement Notes

Return Objective

Calculated based on wants and needs e.g. accumulation of wealth goals for retirement, financing child education etc

The return objective may be single stage or multi stage. eg. the investor may earn income upto retirement agressively investing in equities but after retirement his return objective could be lower focusing on higher income generating assets. this is a multi stage objective firstly to retirement and then post retirement.

If there are multiple goals, the investor may adopt a goals based asset allocation, targeting a certain return for each bucket - personal risk, market risk and aspyration.


Risk Tolerance

1) Willingness to take risk

2) Ability to take risk

Recommendation should not exceed willingness to take risk

Situational profiling:

Take into account:

a) Source of wealth - affects the willingness to take risk. if one inherits the wealth, he has lower willingness to take risk vs entrepreneur who actively earned his wealth and would be more willing to accept risk

b) Measure of wealth - affects both ability and willingness. if one views his wealth is high, he is likely more willing to accept risk. If objectively ones wealth is low, then his ability to tolerate risk is likely lower

c) Stage of life - ability to tolerate risk falls with age

Constraints

1) Time Horizon - if the investor is very young, he has a very long term time horizon and can accept more volatility in this portfolio

2) Liquidity - retired couples who rely on investment portfolio income would need more liquidity and therefore may not be able to invest in equities that dont pay dividends.

3) Tax - the investor may be in a high income tax bracket and therefore would benefit from investments generating returns from capital gains.

4) Unique Circumstances - e.g. special goal to make a payment or donation at a certain date 

Cross Hedging and MVHR

CROSS HEDGE Explained

It is often the case that various assets in the portfolio and exposure to different currencies with imperfect correlation between them creates a natural hedge also known as the cross hedge or proxy hedge or macro hedge. A cross hedge is an indirect hedge as opposed to using forwards to hedge which is direct.

For example historically the Brazilian Real and the Russian Ruble have been closely correlated. A short position in the Real and a long in the Ruble can reduce overall portfolio risk (as measured by volatility). In this case derivatives and forward contracts are not needed and sometimes they are not available or illiquid.

It is important to note however that whenever a cross hedge is used to minimize portfolio risk, basis risk is incorporated into the portfolio which in a sense is produced by the fact that we are assuming that these correlations between currencies will hold in the future.

For example if we were to invest in Russian Ruble Bonds and Turkish Bonds on the premise that they have lower correlation and that the Russian economy is a net exporter of oil and gas while Turkey is a net importer. We would then use cross hedging to reduce portfolio risk by including both Russian and Turkish assets in the portfolio.

Then a crisis happens due to Turkish debts skyrocketing and investors becoming frightened, pulling out of emerging markets in general. This is called contagion. In this case the correlation between the currencies of the two countries can change significantly, now the currencies both fall and correlation increases towards positive 1 as investors sell their Liras and Rubles to purchase USD which is considered safer.

The risk that the correlations between the two currencies changes is the basis risk.

Basis risk is introduced by the cross hedge which is an indirect form of hedging while a direct hedge with a forward contract for example will not produce basis risk.

Minimum Variance Hedge Ratio (MVHR)

When using forward contracts to hedge, often an ideal hedge does not exist and hedging is also often expensive. Finding an optimal hedge that is less than 100% often known as the minimum variance hedge is often the best solution.

an ordinary least squares is typically used.

return in domestic currency = alpha + beta x (FX return) + resitual 

the beta is given as correlaton of (Rfx, Rdc) x std (Rdc)/std (Rfx)

The beta is the minimum variance hedge ratio

in the case of basis risk, it is expressed in the instability of beta.

Note: If I am long USD/AUD, I am long the base currency, i.e. AUD


Example with Rubles and USD

I am a USD investor but am originally from Russia and like to have a little exposure to the local equity market in my portfolio (presumably because I think the Russian equity market is very cheap). I would like to hedge my Russian equity exposure however back to USD because I live in the US.

I note that the correlation between the returns of the Russian stock market in Rubles and the % change in USD/RUR is +0.6 i.e. when the Russian Stock Market goes up the Ruble tends to go up as well most of the time, so they to some extent move together but not perfectly.

I decide I want use forwards, so I would go short a USD/RUR forward but I need to know the nominal amount and I wish to use a minimum variance hedge ratio for this.

I regress Rdc = alpha + beta x Rfx + residual and find the beta of 1.35 fits.

If sport USD/RUR = 0.01666 and I invested $1m then I have 60m RUR invested in Russian stock market. I need to go short USD/RUR forward for the nominal amount 60m RUR x 1.35 = 81m RUR

Because the Ruble and the Ruble stock market is positively correlated, we need to hedge more than the Ruble exposure in order to account for the FX volatility.

Credit Analysis & Concepts

1. Credit Analysis:

When analyzing the fixed income opportunities use the 5 Cs of credit analyst which are

a) Character - how honest are the management and owners? Having they screwed over lenders and creditors in the past? All these sorts of questions need to be answered before contemplating becoming a creditor of the company

b) Capital - how much the borrower has put up in capital into the business. If for example an LBO firm seeks debt financing, it is worth while looking at how much equity the LBO firm is willing to put up from its side and how much capital there is in the business to date. The more equity capital the project has, the safer it is for the creditor to provide financing.

c) Capacity - ability of the business to meet its credit obligations. If there is a cushion to protect companies if the operating performance declines or if the revenues and profits are resilient due to the non-cyclical nature of the business, then the company is more credit worthy.

d) Collateral - if default occurs, the creditors should look at what assets they can use to cover whats is due to them. Banks typically pledge company assets but in the case of fixed income investors they would look at what assets can be recovered after the more senior creditors recover their money and the liquidity of those assets. For example a business with a factory and some real estate issues a bond but also has a bank loan which is guaranteed by a mortgage over the real estate. (the bank would have a senior claim over the real estate of the company in this case)

In this case if the business collapses, the bank can take over the real estate, liquidate it and recover its money but the fixed income investor may be stuck with an illiquid and abandoned brownfield site that would be sold for cents on the dollar materializing in a large loss to the fixed income investor.

e) Covenants - these could be negative (restrictive) or positive (affirmative)

Affirmative covenants are things that the issuer must do like maintain insurance or certain liquidity ratio.

Negative coventants restrict the issuer from doing something that is not in the interest of the creditor like paying large dividends or increasing leverage beyond a certain level.

2. Concepts

It is often worthwhile to understand key investing concepts. Here is a summary:

a) Credit risk has two components default risk and loss severity (also referred to loss given default)

Some fixed income investors use the formula:

credit spread = annual credit loss risk = (probability of default) x (1- recovery rate)

b) Spread Duration - a concept useful to comparing credit risk of bonds especially with a floating rate element. Spread duration measures the price change due to a change in the credit spread.

change in the bond price = change in the bond price due to a change in the risk free rate + change in the bond price due to a change in the spread.

Typically a standard fixed interest bond will have a modified duration equal to the spread duration. This is however not the case for floating rate bonds which have very little duration but could have substantial spread duration.

Spread duration is most useful for investment grade bonds.

Spread risk generally refers to the change in the bond price relative to a risk free bond due to spread widening (Credit Migration). Credit Migration refers to the decline in credit quality of the issuer leading to lower credit ratings and an increased spread.

c) Empirical Duration - is based on regression of actual bond prices and interest raEmpte changes

Effective durations are based on the present value of future expected cash flows should bond yields change either up or down.

Empirical duration tends to be lower than effective duration for investment grade bonds where as for high yield bonds the difference is negligible.

Investment grade investors primarily experience interest rate risk while credit and spread risk is secondary. For high yield bonds investors on the other hand

d) Liquidity Risk - ability to buy or sell quickly in the market at near fair market value.

Options Strategies List

1. Covered Call: Long Stock + Short Call (income strategy)

2. Protective Put: Long Stock + Long Put (insurance strategy, the exercise of the put is near the current stock price, also known as a married put)

3. Collar: Long Stock, Out of the Money Short Call and Out of the Money Long Put

4. Bull Spread:

a) Long Call at X and Short Call at X+Y (Bull Call Spread)
b) Short Put at X and Long Put at X-Y (Bull Put Spread)

5. Bear Spread:

a) Short Call at X-Y and Long Call at X (Bear Call Spread)
b) Long Put at X and Short Put at X-Y (Bear Put Spread)

6. Seagull Spread:

a) Bullish Seagull = Bull Call Spread + Sell Put
b) Bear Seagull = Bear Put Spread + Short Call

7. Butterfly Spread:
 Long Call at X1 + 2 Short Calls at X2 and Long Call at X3 (Bull Call Spread + Bear Call Spread)

Alternatively you can construct a butterfly spread with a Bear Put and a Bull Put

The Butterfly spread is a bet on low volatility that the share price will not go up or down a lot.

A short butterfly spread is a bet on higher volatility

8. Condor Spread: Bull Call Spread and Bear Call Spread. (Volatility Bet)

9. Straddle: Long Call and Long Put Both at the Same Strike Price

10. Strangle: Long Call and Long Put wtih Different Strike Prices

11. Short Risk Reversal: Long Call + Short Put

12. Box Spread: Bear Put Spread + Bull Call Spread

13. Put Spread: Buy Put and Short Call



It is worth while to recall the put call parity relation when considering these:

p+S=c+X/(1+rf)^T
(for European options)

Portfolio Performance Evaluation Risk/Return Measures

	Type of risk measure	Advantages	Comments	Comments 2
Sharpe Ratio	Total Risk		Assumes normally distributed returns, based on the CAPM, slope of the CML	Biased upwards for hedge funds Uses portfolio total risk instead of systematic risk
Sortino Ratio	Total Risk	Good for hedge funds Good for assets with skewed distribution of returns	Improves on the Sharpe Ratio that penalizes for good performance which is incorporated in the up side deviation
Information Ratio (Appraisal Ratio)	Total Risk	Used to measure active performance of mutual funds	Higher information ratio (0.4-0.6) is considered better. The index has zero IR	IR = active return/active risk IR = IC x BR ^ (0.5)
Jensen’s alpha	Systematic	Used frequently to evaluate mutual fund performance	Based on the CAPM
Treynor	Systematic	Overcomes the Sharpe ratio limitation that it uses total risk	Slope of the SML
M squared	Total Risk	The Sharpe ratio is awkward to interpret when it is a negative value. M squared is always positive.	A skillful manager will generate an M2 greater than the return on the market	Rf + SR of asset x Market STD. M^2 measure ranks in agreement with the Sharpe ratio

Taxable vs Tax Exempt Bonds

Note that taxable bonds have a flatter yield curve and in the case of an upward sloping yield curve the investor has less incentive to extend duration as there is relatively less upside in higher duration bonds due to tax effect

Tax exempt bonds generally offer a greater incentive to extend duration compared to taxable bonds. Therefore they would have a steeper yield curve.

A US investor may decide that it is more efficient to place taxable bonds in a tax exempt investment account or a tax deferred one whereas tax exempt bonds can be placed in a taxable account.

Four Types of Liabilities

Type 1 - Known Future Amount, Known Timing

Type 2 - Known Future Amount, Unknown Timing

Type 3 - Uncertain Amount, Known Timing

Type 4 - Uncertain both Amount and Timing

Types of Tactical Asset Allocation

Discretionary - investor modifies his tactical asset allocation according to market valuations e.g. rebalancing from more expensive asset class into a cheaper one

Systematic - use of quantitative models to exploit market inefficiencies e.g. trend following/momentum based approach. If US stocks go up, overweight US stocks

5 C's of Credit Investing

1. Character - credit history of the borrower, reputation etc

2. Capacity - ability to finance debt i.e. net debt/ EBITDA, interest cover etc

3. Capital - factor of shareholders putting up capital. e.g. the size of the downpayment on a house

4. Collateral - assets the creditor can potentially fall back on in an event of default

5. Conditions - e.g. covenants that protect the creditor such as restriction on dividends, maintenance of interest rate cover or net debt to EBITDA ratio

Taxation Summary Table

The below table gives a brief summary of the type of taxation and how they vary with pre-tax returns and investment time horizon.

Tax Type	Formula	As n increases, tax drag:	As r increases, tax drag:
Accrual taxes	FVIF = (1+r(1-t))^N	% increases and amount increases	% increases and amount increases
Deferred capital gains tax	FVIF =(1-tcg)x(1+r)^N + tcg x B	Amount increases and % increase If B<1 then % > t If B = 1 then % = t If B>1 then % < t	Amount increases and % increase If B<1 then % > t If B = 1 then % = t If B>1 then % < t
Annual wealth tax	[(1+r)*(1-tw)]^N	Amount increases and % increases	Amount increases but % decreases
Blended taxation	wattr = pd x td + pi x ti + pcg x tcg R = r *(1-wattr) T = tcg x (1-pi-pd-pcg) / (1-wattr) FVIF = (1-T) *(1+R)^N + T – (1-B) x tcg

Accrual Equivalent After Tax Return = (EOP Value/BOP Value)^(1/N)-1

Foundations 101

Foundations and endowments can be grouped together as insitutions providing support for non-profit activities.

Endowments are typically owned by non-profit institutions such as universities e.g. Harvard University Endowment and are typically viewed as very long term oriented.

Foundations are funded by gifts and investment assets and typically are setup for some specific purpose e.g. funding a scholarship

Private foundations are created by a single donor with specific goals and in the US, the tax systems makes it necessary to have minimum spending levels in order to maintain the privleged tax status. E.g. Gates & Rockefeller foundations. The spending requirement reduces the ability of the donors to use the foundation as a tax shelter.

The endowments are usually created over time via gifts and contributions. The Yale, Harvard and Princeton endowments were grown over centuries.

Foundation Type	Description	Sources of Funds	Decision Making Authority	Spending Requirement
Independent (private or family)	Independent grant making organization	From individual or family	Donor or Trustees	At least 5% of average asset value
Company sponsored	Legally independent, grant making	Annual contributions from profit making corporation or an endowment	Board controlled by sponsors executives	At least 5%
Operating foundation	Provides direct service to a non-profit (instead of grants)	Individual or family	Independent board	Must use 85% of interest and dividend income for institutions programs. In some cases 3.3%
Community foundation	Publicly supported/type of charity	Multiple, public	Board of directors	None

Of the crucial differences it is also noteworthy to mention that foundation tend to have one initial contribution and then exist on the investment income of the contributed assets. Endowments tend to have additional contributions made to them over time and dont face the requirement of a spending rate in the same way as foundations face.

SML and CML

Behavioural Finance Concepts

Prospect Theory - alternative to utility theory, value is assigned to changes in net wealth instead of total wealth and probabilities are replaced by decision weights. Decisions weights are lower than probabilities apart from low probability events in which case it is reversed. (explain why people buy insurance and lottery tickets) Prospect theory points out also that people are not risk averse but loss averse i.e. their losses matter more than the gains.

Bounded Rationality - assumes investors are rational but are subject to limitations of knowledge and cognitive error. Limitation in knowledge and cognitive error lead to satisficing eg rule of thumb decision making

Rational Economic Man = assumes key traditional finance assumption that people have perfect informatio, are perfectly self interested and are fully rational

Utility Theory = traditional finance theory that people maximize their utility subject to a budget constraint.

Utility Theory Axioms = continuiting (if a>b>c then b can be expressed as a combination of a and c), completeness (a is either = or > or < b) , transitivity (if a>b and b>c then a>c), independence (if c is mutually exclusive from a and b, then a>b implies a+c>b+c)

Decision Theory - concerned with identifying probabilities, values and uncertainties of outcomes relevant for a given decision with a goal of using infomation to identify an optimal decision (normative = ideal decision)

Behavioural Portfolio Theory - as compared to the modern portfolio theory under BPT investors construct portfolios in layers and expectations of return and risk profile vary between these layers.

Life Cycle Theory - people are assumed to save and spend money rationally over their lifetime in line with their short term and long term plans.

Behavioural Life Cycle Theory - life cycle theory that incorporates self control, mental accounting and framing biases

Traditional finance theory - assumes rational economic man, that investors are risk averse utility maximizers

Friedman-Savage Double Inflection Utility Function - investors are risk averse at low wealth levels, risk seeking at middle wealth levels and risk averse at high level of wealth.

Adaptive Market Hypothesis - applying theories of competition, adaptation and natural selection to reconcile the efficient market hypothesis. e.g. LTCM used arbitrage strategies that became more popular which led to more competition and LTCM's inability to adapt led to its failure.

Behavioral Asset Pricing - suggests to add a sentiment risk factor to the discount rate i.e. not only account for time value of money and fundamental asset risk

Greeks & Options

Delta of an option is the rate of change of the option price to a $1 change in the underlying price. Delta of a call option ranges from zero and 1 and the Delta of a put option ranges from zero to -1. I.e. put option delta is always negative while the call option delta is always positive.

if the call delta is 0.5, then a $1 increase in the price of the stock will increase the price of the option by $0.5

The delta is the sensitivity of the options price to the price of the underlying which is analogous to the bond price's sensitivity to the bond duration and the stocks sensitivity to the market as manifested by the stock beta.

Theta of an option represents the sensitivity of the option price to the change in time. Theta values are always negative for long options positions.

For example if theta is -0.5 then for every day the option will lose $0.5 in price.

Gamma is the sensitivity of the options delta to the underlying price. E.g. if Gamma is 0.5, then if the underlying asset price increases by $1 then delta will increase by 0.5$

Gamma = (change in delta)/(change in the underlying asset price)

Gamma is the highest value when the option is trading at the money. 

Vega - measures the change in the options price that would result from a 1% change in the implied volatility of the underlying security.

Price of the Underlying	At the money	Deep out of the money	Range	Short options	Other notes
Delta	Call options have delta of 0.5 Put options have delta of -0.5	Call & put options tend to have delta of zero especially closer to expiration	(0-1) for call options and (-1-0) for put options	Opposite sign to long positions	Deep in the money calls have delta close to 1 Deep in the money put options have delta close to -1
Gamma	highest	Zero	Always positive or zero	Negative	Gamma is also high closer to option expiration. Gamma is highest when the option is at the money
Theta	Highest for short term options	lower	Negative for long calls and long puts	Positive for short calls and puts	Long term options have low theta High volatility stocks have high theta

• deep in the money calls have delta of 1 and deep in the money puts have delta of -1
• if a long put and long call have identical features, then the sum of the absolute values of deltas will equal 1
• a call option on EUR/USD is identical to a put option on USD/EUR

Hedge Fund Strategies List and Terminology

1. Portable Alpha - is separating an active managers alpha, the return from security selection within an asset class from beta. Typically this is done by using derivatives to eliminate beta from the exposure. The beta exposure is added from a different asset class. Typically a specialist manager can generate alpha in one country say Turkey while a US investor would take beta exposure to the S&P 500

2. Alpha Beta Separation - separating a portfolio into a strictly passive (beta) portfolio such as an index and an alpha seeking portfolio, e.g. market neutral fund. Here the alpha and beta are still generated based on same index or asset class.

3. Market Neutral - shorts and longs matched in portfolio to produce overall beta zero portfolio that is not correlated the market. The goal is to generate alpha on the long and short side, generating an absolute return uncorrelated with the market. Allocating to this strategy given its lower correlation with the market would be a good diversify to a portfolio that has assets that are correlated with the market.

4. Long Short - traditional hedge fund strategy that combine long and short positions and leverage

5. Global Macro - investing across the liquid asset asset classes based on macroeconomic principals and top-down approach.

6. Event Driven - includes Risk M&A Arbitrage and Distressed Securities

7. Managed Futures - carried out normally as commodity pools or commodity advisor funds (CTAs). These managers take direction bets on the price direction of commodities and interest rates.

8. Short Extension Strategy - long short strategy whereby the Longs would constitute a greater exposure than the shorts. e.g. long 100% and short 20%

9. Pairs Trading - two securities are traded, one long and one short with equal matching amounts. E.g. one could go long one stock and short another for the same dollar amount in the same industry with a view that one firm is better positions on the market or for some reason is likely to outperform thus generating alpha.

10. Equitizing - giving systematic risk to a market neutral portfolio by using derivatives. ETFs may be another insrument of equitizing the portfolio.

11. Completeness Fund - passive or semi-active style that has the same risk and characteristics as the index which still generates value added.

Non- Financial Risks

Operations Risk - Risks of human error, fraud or misconduct that were failed to be prevented by internal controls. Natural disasters are also included.

mitigation: independent audits of systems used to mitigate risk (both internal and external), remote back up systems

Model Risk - risk of using a model to monitor investments eg model does not take into account relevant variables for he task.

mitigation: regularly review model assumptions, list of variables, making sure the correct-upto date and correctly adjusted inputs are used

Regulatory Risk - the risk that laws or regulations will change and affect the nature of an existing or planned transaction. Regulatory risk for transactions increases with the number of jurisdictions that they must comply with.

Herstatt Risk or Settlement Risk - risk that the counterparty cannot make a required payment or delivery. The risk is named after a German bank that failed to deliver on tranactions it initiated during the day after it was shut down by regulators.

Legal Risk - the risk that the counterparty does not honor a contract or the contract or a provision is not enforceabe. This one also includes the risk of a lawsuit brought by the client or the counterparty.
Legal risk tends to increase when counterparties are located in different countries.

Tax Risk - risk of changes in tax laws or the enforcement of existing ones. Complex securities, structures or deals increases tax risk.

Accounting Risk - risk arising from difference in accounting rules and their application. Risks could arise from aggressive accounting, managed earnings or disparaties of in accounting rules.

Sovereign Risk - risk that the government defaults on its debt either through lack of willingness or abiliy to pay

Political Risk - either minor or major changes in government that affect the invetment environment within the country.

ESG Risk - Environmental, Social and Governance risks. Social risk ivolves changes in workplace standards, human resource practices and employee policies and procedures.

Performance netting - the loss in return ot the investor when paying for positive performance in one portfolio and losing as much in another portfolio.

Mean Variance Optimization Limitations

Mean Variance Optimization (MVO) is currently one of the mainstream asset allocation approaches used in modern finance and is a core component of the modern portfolio theory. The theory distills securities to just return and risk (as measured by security price standard deviation) and assumes investors seek the highest return for the lowest level of risk (again as measured by the standard deviation of portfolio returns)

Today computer programs take into account the correlations between asset class returns to identify combinations of asset classes that offer highest possible returns for a given level of acceptable risk.

Key assumptions behind MVO:

1. Risk averse investors
2. No taxes or transaction costs
3. Investor returns are normally distributed
4. All returns, correlations and variances are known

As you can see these assumptions are extremely strong and discredit the approach significantly

Here are just a few criticisms

(CRISLS)

1. Concentrated positions - MVO produces highly concentrated asset allocation positions that may not be acceptable for investors

2. Investors care not only about returns and variance but other factors as well

3. The MVO models are highly sensitive to small changes in the inputs

4.  Sources of risk may be different so in essence the MVO asset allocation could be poorly diversified due to high exposure to a single risk source.

5. No Liabilities - MVO does not have a mechanism to account for liabilities

6. Single period model

Asset Classes - What Are They?

Asset allocation and the theory behind it is a critical cornerstone in portfolio management today but behind all the discussions on asset allocation we should keep in mind the key properties to look for in identifying a true asset class:

(DICHM)

1. Diversifying - the name says it all really. The asset class identified should not be 100% correlated with any other

2. Investable - there is just no point in identifying an asset class that one cannot gain any exposure to

3. Group Global Investable Assets: Together with other asset classes the group should constitute all or close to all investable global assets.

4. Homogenous - the assets within an identified asset class should behave in similar ways. i.e. don't put corporate bonds with inflation linked fixed income securities together in one asset class as they behave very differently (when rates rise due to higher inflation, corporate bonds will likely fall significantly more than inflation linked securities that will increase coupons in line with inflation)

5. Mutually exclusive - the asset class should not some of the assets that are already in another asset class

What Makes a Good Benchmark?

Whether you are managing a Fund or just a personal portfolio, selecting the right benchmark could be important as you seek to evaluate your own performance. Below are the core characteristics to look for in a benchmark.

For the sake of example, I add a little personal comment on how I feel the S&P 500 works as a benchmark to Berkshire Hathaway stock returns given that they use it as their guide.

• Appropriate (A) 

the benchmark needs to be appropriate. you can't use a basket of US large cap insurance stocks to track performance of an african insurance stock. here it is a question whether S&P 500 with a sizable weighting in technology is appropriate for BRK which is a collection of companies with relatively little technology exposure. It kind of feels that S&P 500 does not fit well here

• Investable (I)

S&P 500 does well here. You can simply use a low cost ETF such as the Vanguard VOO

• Measurable (M)

S&P 500 stock returns are openly available and in terms of being measurable there clearly is no argument here

• Accountability (A)

warren buffet did say that his managers are incentivized to outperform the S&P 500 and he himself as put his reputation on the line in order to succeed in this task. certainly these guys "own" their benchmark

• Representative of the Investor's Views (R)

this one is more difficult. Berkshire Hathaway is clearly focused on high quality large cap value as a style of investing and research suggests that this style does closely match the BRK performance. it is therefore difficult to take S&P 500 - a broad index of US firms as representative of the BRK style of investing and approach. BRK also has some investments abroad which is also a factor to consider

• Unambiguous (U)

the S&P 500 stocks are closely followed and rarely do companies get kicked out or included in the index. certainly it does not feel ambiguous 

• Set Out in Advance (S)

Warren Buffet has set out S&P 500 as the benchmark many many years ago. if I'm not mistaken from the outset. It certainly seems like the benchmark clears this hurdle

Asset Allocation Ideas

Asset allocation according to the recent CFA survey is one of the most critical aspects in asset management, but what exactly is asset allocation and what does modern finance theory recommend when allocating capital across the different asset classes available to investors today.

Asset allocation may be defined as an investment strategy that aims to balance risk and reward by apportioning assets in accordance with the investors risk profile, investment horizon, return requirements and other contraints as may be specified in the investors investment policy statement (IPS).

Asset allocation allows the investor to identify the right mix between the asset classes available and then select a passive or active investment strategy within each asset class. An institutional investor may have access to different asset classes than the individual investor because they may be able to gain access to transactions that the individual investor may not. An example of this is Berkshire Hathaway doing deals during the great financial crisis when they could strike deals with Goldman Sachs for example that was lucrative but only available to them and not the general public.

Another example could be hedge fund and LBO fund investments where the minimum entry target committment can be $5m and therefore many individual investors are not able to participate.

The two traditional asset classes are the equity and fixed income markets. The alternative asset classes are real estate, hedge funds (all types), commodities (e.g. gold futures), private equity and venture capital. Most of these are highly illiquid, have large minimum investment size requirements and require the investor to be knowledgeable with expertise in evaluating managers for example.

There is a variety of methods that have been developed over the years to generate asset allocations either taking into account liabilities or not. Here is a summary of the main ones:

1. Mean-Variance Optimization (MVO) - developed in the 1950's by Harry Markowitz, this is perhaps the most common approach to developing an asset allocation. It builds on the key concepts of his modern portfolio theory (MPT) whereby one needs to not only look at the best risk vs reward ratio but also the correlation of the assets in the portfolio as well and thereby look at the risk and reward characteristics of any asset in the context of the overall portfolio.

The MVO uses the objective function as follows:

$$U_m=E\left(R_m\right)-0.005\lambda {\sigma }_m^2$$

where

U_m = the investor’s utility for asset mix (allocation) m

R_m = the return for asset mix m

λ = the investor’s risk aversion coefficient

${\sigma }_m^2$ = the expected variance of return for asset mix m

For example if the investor risk aversion coefficient is 2, expected variance is 20% and the expected return on the asset mix is 10% then the Um = 10% - 0.005 x 2 x 20% = 10%-0.002=9.8%

The formula is used to generate a set of asset classes that will generate the highest utilities from asset allocations. These are typically generated in the form of an efficiency frontier that shows the appropriate allocation for each specific require return and acceptable level of risk. Low acceptable levels of risk typically generate a high cash and fixed income component while high required risk will often allocate greater portions of the portfolio to equities and alternative asset classes. (emerging market equities are considered riskier and therefore have a higher expected return as an asset class compared to developed market equities)

Key criticisms of the MVO model

a) small changes in inputs may lead to large changes in outputs
b) asset allocations tend to be highly concentrated
c) many investors are concerned with not only mean and variance of returns which is the focus of the MVO approach
d) sources of risk may not be diversified even though assets are
e) does not take into account liabilities
f) single period approach which also has no way of dealing with trading costs and taxes


2. Monte Carlo Simulation  - this is a method that is typically used to complement the MVO because the MVO is a single period framework which is a disadvantage in real life. The method typically uses simulation software to identify the most optimal asset allocations by applying assumptions about probabilities of vairious outcomes 

3. Reverse Optimization - this technique is effective in dealing with the MVO criticisms a) - c)
In the MVO the optimizer uses the returns, variances and correlations to generate an optimal asset allocation. The reverse optimization identifies an optimal asset allocation over some period of time and then uses that allocation to produce implied asset returns that may be used in forward looking optimizations.

4. Black-Litterman Model - developed in the early 1990s. The model effectively uses the reverse optimization model to generate returns and then adjusts them as per the specific investor's views while still working well as an optimizer.

In practice most of these approaches are used via specialized software but the individual investor can learn from the broad approaches. The above are just the asset only asset allocation approaches but the individual or insitutional investor may have liabilities that need to also be taken into account. We will cover that in a separate post.