Question

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.
How to explain generally the Markowitz model and Black-Litterman model.

Answer 1

Part I

Markovitz's Model
Harry Markovitz recieved a noble prize in economics for his work on "Modern Portfolio Theory". His work has brought about great changes in the asset management field, and the theory is extremely useful in the field of porfolio management.

Modern portfolio theory focuses on two major concepts :

• The investor should look for increasing returns on the risk taken.
• If the porfolio is diversified with unnrelated assets, it can reduce the risk for the investor.

It is also called the passive investment approach, this is because the investor can achieve a perfect risk for repurchasing the portfolio which has a substantial value, and then can look forward to growing it.

Concept of maximum return and minimum risk

The value of an asset such as share price, dividends or any other capital flow is referred to as returns.

Standard deviation helps to measure risk reasonably because an investor looks for a constant and regular increase in his investment, and not large movements, which can result in a loss.

The deviation of the standard or risk can be defined as the average cost of a property on a variable basis. If the price of an asset experiences 5% deviation its mean and the expected return on an average is 10% , then the actual return can be expected to be anywhere between -5% and 15%.

Practical application

Markowitz's portfolio theory can be very useful in the practical scenario as well, we look at two portfolio of assets with an average return of 5%, the risk of the porfolio A is at 3% and that of portfolio B is at 8%. A prudent investor in this case whill chose portfolio A since with roughly same average return, the risk of the portfolio is lower.

The risk is an important component in the risk-return theory, which functions on a direct relationship between both risk and return.

Looking at the above example an investor might be inclined to chose portfolio B since it can offer 13% return, however one needs to look at the downside of -3% as well.

As a result, the investor should ideally look at portfolio B which provides an upside of 8% and a downside of 2%.

Limitations of Markovitz Model

1. Large data requirement for calculations

2. Complex computations

3. Can't function in an a scenarios where the portfolio is not diversified

Part II

The Black-Litterman model

Fischer Black and Robert Litterman developed an asset allocation model. The model aimed at combining ideas from Capital Asset Pricing Model (CAPM) and the mean-variance optimization model created by Markovitz.

Black-Litterman model acts as tool for investors to compute the optimal portfolio weights subject to specific parameters.
Prior to the Black-Litterman model, the investors used the expected return on assets with Markowitz's model to generate portfolio weights The application of the model has universally faced a challenge that is to compute the reasonable estimates for expected returns, covariance can be easily computed though.
Assumptions of the model
The following 2 assumptions forms the base of the model :

• First, the model makes an assumption the probability of all asset returns is same. Usually normal distribution is used however the investors can also use different types of distributions.
• Second, the conditional distribution of the asset, variance and investor views are unknown components.

How to use the model

Step 1: Derive market returns using the CAPM model

Step 2: If investors indirectly agree with the returns, they can use the arbitrage Weights by the Black-Litterman model to create their optimal portfolio.

Step 3:  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.

The model helps to combine allocations as a result of the market market equilibrium as per the Capital Asset Pricing Model (CAPM) along with portfolio managers’ views.