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. 

Relative Value Models

There are several models that have been developed to help us investors assess the basic questions that is often asked: "Is the market cheap?"

Here are several you probably should know:

Fed Model - this one is the simplest, developed by Edward Yardeni who noted the relationship betweent the US treasury bond yields and the earnings yield on equities. The model states that one should compare the forward earnings yield of the market (e.g. S&P 500) vs the 10 - year government bond yield.

If the forward earnings yield is greater than the 10-year government vbond yield, the market is cheap. Otherwise its expensive.

The model appears to be easy to use and is within the spirit of the discounted cash flow approach but there are issues with it. For one it ignores the future growth of the earnings yield. One stock market may have a big tech component and have a higher prospective future growth rate in earnings yield while another may be dominated by mature traditional businesses with low earnings growth but a higher earnings yield today. (growth stocks vs. value stocks)

Another issue is risk. The equity risk premium is totally ignored because you are essentially comparing a risk free investment in bonds with an investment in a basket of stocks which may be depressed for a prolonged period of time for various reasons such as regulation, poor government policies etc.

The last criticism is that it compares a real yield (since it is yield in the current period at current prices) with a nominal yield that is generated mainly in future periods.

Yardeni Model - this model attempts to address the above criticisms of the Fed Model.
this model compares the forward earnings yield of the stock market to A-rated corporate bond yeild - d x LTEG

where LTEG is the long term earnings growth rate and d the weight investors assign to future earnings growth projects which is historically 10%.

so if our forward P/E is 20x, our forward earnings yield is 5%

if our LTEG = 5%, d= 10% and yb =3.5% then
yb-d x LTEG = 3.5%-0.5% = 3% < forward earnings yield = 5%  therefore the market is cheap!!

Cyclically Adjusted P/E Ratio (CAPE) - two kind men, Campbell and Schiller developed another way of trying to assess the market valuations based on the recommendations set out in Security Analysis (1934) text by Graham & Dodd.

The CAPE is a P/E ratio calculated over a 10-year period and adjusted for inflation. One can then compare it to current P/E levels to assess whether the market is currently cheap or expensive.

Tobin's Q and Equity Q - these methods wre originally developed by Brainard and Tobin to assess both market valuations and also capital investment decisions.

The Tobin's Q formula is as follows

Tobin's Q ratio = (Equity Market Value + Liabilities Market Value) / (Total Assets at Replacement Cost)

The idea is that an undervalued company would have a Tobin's Q of less than 1. Such a firm could be considered a good investment.

In some cases an alternative formula is used called Equity Q

Equity Q = Equity Market Value / (Total Assets at Replacement Cost - Market value of Liabilities)

Emotional vs Cognitive Biases (most complete list)

In order to become a better security analyst, I recommend to spend some time and read about the latest field of finance called behavioural finance.

All investors are human beings and we are all prone to making mistakes due to phsychological factors. The two main types of behavioural investor biases are cognitive and emotional.

Cognitive biases are rule of thumb biases which are more to do with faulty thinking by investor whether based on misinterpretation of facts or not using facts available.

Emotional biases - these are distortions in cognition and decision making due to emotional factors.

It is worthwhile taking a brief moment and review the full list of biases that are out there. Over time I think you will recognize when you as an investor will be affected by such a bias. In an effort to be a rational investor, I think this is worthwhile.


What behavioral finance also tells us is that if we are able to identify whether the bias is cognitive or emotional we can then deal with it more appropriately. The theory states that if the bias is emotional, one cannot try to resist it by educating the client for example but must adapt. ( e.g. no point in arguing with an emotional girlfriend, you have to adapt to minimize damage)

On the other hand if the bias is cognitive, then you can adapt through education and discipline to avoid it. 

Behavioral finance also teaches us something about standard of living risk. The theory goes that if the standard of living risk is low, you can adapt your biases more because you can afford to risk more of the capital because your lifestyle is unlikely to be jeopardized. 

On the other hand if your wealth is low and you have a high standard of living risk, then you have to restrain yourself and moderate as you cannot afford to take excessive risks. 

Cognitive Errors

Belief Perseverance Biases (holding on to one's beliefs even though data suggest otherwise)

1. Representativeness Bias - using heuristic approach to estimating outcomes. There are actually two intepretations of this bias:

a) Base rate neglect - when an investor fails to estimate the approapriate probability of an outcome based on the big picture/general information about an outcome. e.g. you focus on some very specific points about an investment opportunity and apply too much weight on them vs the larger issues such as long term future of the industry the company is doing business for example

b) Sample size neglect - when you base your decision making estimations on a small sample. e.g. junk bonds have done extremely well over last few years. since i have not witnessed an environment of prolonged rising interest rates and widening credit spreads, i may estimate the probability of negative returns on junk bonds as low

2. Illusion of Control Bias - tendency to overestimate ones ability to control events
e.g. employee investing in employer stock. by doing so they feel as a manager of the business they have some power over the success of the enterprise although this may not be the case.

3. Conservatism Bias - tendency to revise beliefs insufficiently when faced with with new data

e.g. the fundumentals of the industry and the business have deteriorated significantly which means the prospects of the business are no longer viable. nevertheless the investor observes that the price has not yet moved down significantly. It would make sense for the investor to rationally assess the situation and sell down the position in order to invest in another business which has better economics and better prospects. Instead the investor reduce his exposure by only 10% and decides to hold on to the remaining investment even though his rational analysis suggests that the prospects are poor. 

4. Confirmation Bias - tendency to interpret and favor data that confirms pre-existing beliefs

e.g. an investor really likes a specific common stock investment. when doing research he observes that the company management has been successful a few years ago when working at another company. he ignores the fact that the fundumentals of the business have been deteriorating but ascribes great value in the management team and its past track record of running a different company

5. Hindsight Bias - tendency to view an event as predictable once it has already occured even though there may not be any data to suggest this. 

Information-Processing Biases

1. Framing Bias - making different decisions on same subject depending on how the choices are presented

2. Anchoring and Adjustment Bias - tendency to react too much to the first information offered. e.g. investor does not want to sell at less than cost a share in a company even though the intrinsic value of the share may be above the price it currently trades at. 

3. Mental Accounting Bias - tendency to value assets and money differently depending on the mental account they are located in. 

4. Availability Bias - making decisions based on ability to recall past events. e.g. if you did well in beverage company stocks investments in the past, you may remember this experience fondly and in the future you are therefore more likely to be inclined to invest in this sector than actual hard data would suggest you to do otherwise. 

Emotional Biases

1. Loss Aversion Bias - tendency to avoid losses at any cost. if you are offered $10 with probability of 50% or $5 for sure, theorecally you should be indifferent but in reality investors tend to avoid losses even though risk-reward calculation should suggest otherwise.

Loss aversion is basically selling the winners and keeping the losers. 

There is also a concept of myopic loss aversion which refers to group loss aversion whereby investors stay away from risky assets which as a result generate a premium return and trade at discounts. 

2. Overconfidence Bias - when an investor applies greater confidence in his judgements than he should objectively do. 

e.g. you make a lot of money on an internet stock investment and then you start aggressively investing in internet stocks assigning too much value on ones own judgement than otherwise would be rational. 

(note that this is not the same as illusion of control bias which is more about "control")

3. Self-Control Bias - inability to delay gratification. e.g. failing to save for retirement

4. Endowment Bias - tendency to ascribe more value to assets that you own.

e.g. classic case is when you decide to sell your house but you lived there for a long time, lots of memories and you ascribe more value to it than you would for a similar house on the market
e.g. another example is an inherited concentrated equity position which rationally one should sell down in order to achieve greater portfolio diversification, risk tolerance goals and investment goals  

5. Regret Aversion Bias - when you do nothing out of fear that something will go wrong and you will come to regret it

e.g. avoiding investing in common stocks just because your friend lost all his money in the stock market

typically regret aversion leads to herding behaviour where one invests alongside other investors he trusts or based on some recommendations. one may also hold on to a losing position due to regret that as soon as the investors exits the position the the security will recover

6. Status Quo Bias - whereby the individual is more comfortable to do nothing rather than make a change.

e.g. this bias causes the investor to do nothing even though it is not optimal to do so. an example is rebalancing the portfolio allocation, selling down equities that have gone up and investing more in junk bonds that have gone down in order to maintain the optimal portfolio asset allocations 

Capital Markets Expectations Biases

1. Appraisal (Smoothed) Data Bias - for less liquid securities, appraisal based valuations are used which distorts true volatility of asset prices with standard deviation being biased downward as a result, correlations with other assets are likely to be lower than the true correlations.  

2. Regime Switching Bias 

3. Data Mining Bias - searching for patterns in data to find some statistically predictive relationships. These patterns may not have any predictive value however. 

4. Time-Period Bias - selecting time period for research that affects significantly the outcome of the research

5. Survivorship bias - whereby returns maybe biased upwards as only surviving successful hedgefund performance is included where as the funds that went out of business with poor performance is included. 

6. Prudence trap - tendency to revise down forecasts (sometimes to avoid being extreme)  

7. Disposition Effect - tendency to sell winners too soon and hold losers too long in order to avoid realizing losses 

8. Halo Effect -  extends favorable evaluation of some characteristics over others. may lead to extrapolation of past returns into expected returns 

9. Gamblers fallacy - mean reversion fallacy. if you flip a coin 10 times and each time its heads, then you believe the 11th time its highly likely that it will be tails even though the probability is still 50% that it will be either of the outcomes  

10. Anchoring trap - tendency of the mind to apply disproportionate weight to the first information provided. e.g. analyst sticks to original forecast even though new events should force him to adjust his forecast

11. Recallability Trap - forecasters taking into account to much recent events. e.g. forecasters too influenced by recent disasters or financial crisises.  

12. Confirming evidence trap - applying more weight to evidence that supports the analyst's pre-existing point of view. 

13. Over confidence trap - tendency of individuals to overestimate the confidence of their predictions about the future

14. Status Quo Trap - forecasters using data from the past to extrapolate the future

15. Home Bias - preference for investing in securities listed in the home country (AKA home country bias) 

16. Look-back bias/ Hindsight bias - bias associated with selective perception and retention. Outcomes that did occur are more evident than those that are yet to occur. When we look back we do not have perfect memory and fill in the gaps with what we prefer to believe. 

17. Familiarity bias - underestimating risk because of familiarity. e.g. employees underestimate the risks associated with investing in their employer stock

18. Self attribution bias - taking credit for successes and assigning responsibility for failures to others

19. Self-control bias - inability to delay gratification. e.g. spend down instead of saving for tomorrow 

20. Stale price bias - bias arising from using prices based on illiquid securities that rarely trade

21. Conjunction fallacy - belief that two events together occuring is more probable than a single event in isolation 

22. Social Proof - a belief that individuals are influenced by the beliefs of others or the group. An example is where the investment committee members fail to properly discuss decisions and the chairman's view effectively determines the committee preferences. 

23. Herding bias - whereby investors follow others rather than making own decisions or are heavily influenced by others. Herding seems similar to Social Proof, but Social Proof concerns more the group level such as investment committee or a board of directors whereas herding is more about the decisions of the individual

24. Recency effect - tendency to apply too much weight to recent events to make investment decisions.

25. Transcription errors - errors associated with collection and recording of data which may be magnified if this is driven by a bias. 

Behavioural finance is now a big part of the CFA curriculum and is more accepted than ever before by the investment community.