Question

Write up a document explaining the Markowitz model and Black-Litterman model. The document should be in PDF format. Note that Word 2010 and 2013 can save in / print to PDF format. About 500-1000 words (2-4 pages double-spaced) is fine. You can use the example in the Excel template if you feel that helps you explain more clearly. Note that detailed mathematical explanations or derivations are not required.

The document should explain i) what the Markowitz model would suggest that investors do (i.e., how one should invest to achieve a certain investment goal – e.g., 15% expected return – in the 5 country portfolio example, ii) limitations and pitfalls of the Markowitz model, iii) potential mitigations, iv) what the Black-Litterman model does, and v) why it does that.

The explanations should be at a level that could be understood by a finance professional not familiar with linear algebra and the Black-Litterman approach. The tone should be professional but as free of jargon as possible. I will award grades for clarity and accuracy of exposition and overall presentation of the document.

Answer 1

Markovitz's Model
In 1952, Harry Markowitz presented an article on "Modern Portfolio Theory," for which he received a noble price in economics. His innovations have greatly changed the field of asset management, and his theory is seen as a cutting edge in portfolio management.

There are two main concepts in modern portfolio theory;

The goal of any investor is to increase returns on any risk

The risk can be reduced by creating a diversified portfolio of unrelated assets

Other names for this approach are the passive investment approach, because you create the perfect risk of repurchasing the portfolio for the vast asset with substantial value, and then wait until you are proactive and grow.

Maximum return - minimum risk
We will briefly define return and risk. Returns are treated as the value of any asset, like the price of a share, and for any capital inflow, such as dividends.

Generally standard deviation is a reasonable measure of risk because we want a constant increase, but not large oscillations, which can end up being a loss.

Risk is defined as the average variable cost of a property, called deviation of the standard. If the price of an asset is 10% deviation from the average and the average expected return of 8% is expected to be between -2% and 18%.

In the practical application of Markowitz's portfolio theory, suppose that there are two portfolios of assets with an average return of 10%, portfolio A has a risk or fixed deviation of 8% and portfolio B has a 12% risk. Since both portfolios have the same expected return, any investor will choose to invest in portfolio A because it has the same expected return as portfolio B but has lower risk.

It is important to understand the risk; This is a necessary consideration because without it there would be no expected reward. Investors are compensated for risk taking, in theory, higher risk, higher returns.

Going back to our example above, it might be tempting to assume that portfolio B is more attractive than portfolio B. Since portfolio B has a higher risk of 12%, it is likely to have a return of 22%, which is possible but may also be evidence of -2% return. All things being equal, it is still desirable to have a portfolio with an expected range between + 2% and + 18%, as this will help you achieve your goals.

The Black-Litterman model

The Black-Litterman model is an asset allocation model developed by Fischer in 1990
Black and Robert Litterman at Goldman Sachs. This model combines ideas from capital
The Asset Price Model (CAPM) and Markovitz's mean-variance optimization model
Provide a tool for investors to calculate optimal portfolio weights under specific parameters.
Before the Black-Litterman model, investors would enter the expected return on assets
In Markowitz's model to create portfolio weights. However, the complex model is often
Weights have returned to public investors, particularly investors who don't understand
Comments on how the market or certain assets will operate in the future. The Black-Litterman
The model was developed to provide neutral weights for adjustable investors
According to their views on the market.
Before applying the model, one must understand the two main assumptions behind it First, the model assumes that all asset returns follow the same probability distribution
(Usually the normal distribution is selected, but investors can choose any distribution that seems appropriate).
Second, the variance of the prior and conditional distribution of the actual mechanisms of the asset
And investor views are unknown.
To begin using the model, investors first derive market returns
The CAPM model. If investors indirectly agree with the returns, they can use the arbitrage
Weights by the Black-Litterman model to create their optimal portfolio. However, if
Investors do not accept the market returns provided by CAPM and then they have to use it
The Black-Litterman model, which adjusts to neutral weights according to investors' views. There
There are two types of market scenarios - absolute or relative. In full view, investors mention
The percentage return they believe a particular asset will provide (ie. X% returns on property 1).
In relative terms, investors compare one asset periodically with another asset (ie, asset 1 yields higher returns)
Return x% rather than property2). For each view, investors should specify the confidence level
It shows how confident they feel about their ideas.
The Black-Litterman model reveals investor opinions and market equilibrium
Terms of probability distributions. It uses a Bayesian approach to create a probability
The distribution of expected returns by using the CAPM equilibrium distribution as a starting point
Then incorporates investors ’views on supply. Using indirect returns from CAPM
Adding to the sights of investors earlier and later, you can get a back distribution.