Portfolio Management

We all dream of beating the market and being super investors and spend an inordinate amount of time and resources in this endeavor. Consequently, we are easy prey for the magic bullets and the secret formulae offered by eager salespeople pushing their wares. In spite of our best efforts, most of us fail in our attempts to be more than average investors. Nonetheless, we keep trying, hoping that we can be more like the investing legends – another Warren Buffett or Prashant Jain. We read the words written by and about successful investors, hoping to find in them the key to their stock-picking abilities, so that we can replicate them and become wealthy quickly.

Cash flows Vs Growth Prospects Vs Market Timings

The most important steps in Portfolio Management/Investment Management are:
1. Understanding the requirements (needs and preferences)
2. Portfolio Construction (Asset/security allocation and selection)
3. Evaluate portfolio performance
 
The most important concepts in portfolio/Asset management is Asset/security selection and Asset allocation. Generally, a 80-20 concept is followed in Portfolio management where in 80% are used in Beta generation (that is, in line with market) and 20% are used in Alpha generation (that is, used for beating the market). Generating return is not the only objective of a portfolio manager but generating a risk adjusted return with a downside protection is the sole objective of a portfolio manager.

So, in this case Portfolio Manager A has performed well overall as he has beaten the benchmark consistently (both in upturn and in downturn), whereas Portfolio Manager B has beaten the benchmark only in upturn and not in downturn.

Modern Portfolio Theory (MPT)

Most important theory in portfolio construction developed by Harry Markowitz  MPT says that it is not enough to look at the expected risk and return of one particular stock. By investing in more than one stock, an investor can reap the benefits of diversification - chief among them, a reduction in the riskiness of the portfolio. MPT quantifies the benefits of diversification, also known as not putting all of your eggs in one basket.

E(R)=0.4*.11+0.6*.25=19.40%

Sd(P)=sqrt((0.4^2)*(0.15^2)+(0.6^2)*(0.20^2)+2*(0.4*0.6)*(0.30*0.15)*(0.30))=14.94%

Therefore, due to two stocks and a low correlation we achieved diversification and our risk based return increased. We keep on changing weights between the stocks and form a curve.

We keep on adding assets and form a new efficient frontier with different weights assigned. We keep on forming different portfolios and keep them plotting on the efficient frontier, say for example:

So, we form the so called efficient frontier .So say a investor requirement is earning a return of 11% with  SD of 4% we can form a portfolio with combination of portfolio D&E.

Conclusion

The gist of MPT is that the market is hard to beat and that the people who beat the market are those who take above-average risk. It is also implied that these risk takers will get their comeuppance when markets turn down. Again, investors such as Warren Buffett & Prashant Jain remind us that portfolio theory is just that - theory. At the end of the day, a portfolio's success rests on the investor's skills and the time he or she devotes to it. Sometimes it is better to pick a small number of out-of-favor investments and wait for the market to turn in your favor than to rely on market averages alone.

The Sharpe ratio, Treynor ratio and information ratio are all common ratios for evaluating investment managers and investment portfolios. Each of these measureos can be used ex post to evaluate past performance, or they can be used ex ante to help investors make portfolio decisions based on forecasts for various investment alternatives.
 
The Sharpe Ratio

The Sharpe ratio is one of the most common metrics for evaluating portfolios. The Sharpe ratio is calculated by dividing the mean excess return of the portfolio by the standard deviation of the excess return. In other words, this ratio measures the “reward” we can get for a particular level of variability or “risk”. The equation for calculating the Sharpe ratio is:

Sharpe ratio=R(P)-Rf/SD, R(P)=portfolio return, R(f) =risk free retun, SD=stnadard deviation

Bigger is better for the Sharpe ratio. High-reward and low-risk result in a relatively large Sharpe ratio, whereas low-reward and high-risk result in a relatively small Sharpe ratio.

The return-to-standard-deviation ratio is 0.5 for Asset A, and 0.45 for Asset B. Based on these ratios, we might conclude that Asset A is the superior investment. However, if we assume a risk-free rate of 3%, then the true Sharpe ratio calculation gives a different answer. If we properly deduct the risk-free rate from the total returns, we find that the Sharpe ratio of Asset A is 0.25 and the Sharpe ratio of Asset B is 0.30. Therefore, the Sharpe ratio suggests that Asset B is the superior investment.

Sortino Ratio

A ratio developed by Frank A. Sortino to differentiate between good and bad volatility in the Sharpe ratio. This differentiation of upwards and downwards volatility allows the calculation to provide a risk-adjusted measure of a security or fund's performance without penalizing it for upward price changes. It is calculated as follows:

Sortino Ratio=R(P)-Rf/SD(d),SD(d)=SD of Negative Asset Returns

The Sortino ratio is similar to the Sharpe ratio, except it uses downside deviation for the denominator instead of standard deviation, the use of which doesn't discriminate between up and down volatility.
 
Jensen's Alpha

A risk-adjusted performance measure that represents the average return on a portfolio over and above that predicted by the capital asset pricing model (CAPM), given the portfolio's beta and the average market return. This is the portfolio's alpha. In fact, the concept is sometimes referred to as "Jensen's alpha."

Jenson's Alpha=R(p)-(R(f)+Beta*(R(m)-R(f)))
 
The basic idea is that to analyze the performance of an investment manager you must look not only at the overall return of a portfolio but also at the risk of that portfolio. For example, if there are two mutual funds that both have a 12% return, a rational investor will want the fund that is less risky. Jensen's measure is one of the ways to help determine if a portfolio is earning the proper return for its level of risk. If the value is positive, then the portfolio is earning excess returns. In other words, a positive value for Jensen's alpha means a fund manager has "beat the market" with his or her stock-picking skills.
 
The Treynor Ratio

The Treynor ratio is similar to the Sharpe ratio, but CAPM beta is used in the denominator rather than the standard deviation. This is an important difference. Since the Treynor ratio uses only the non-diversifiable risk as to the denominator, it should be used for evaluating funds or assets which are being added to a portfolio that is already well-diversified. 

The Treynor ratio is calculated using this equation:

Treynor ratio=R(P)-Rf/Beta

As with the Sharpe ratio, a larger Treynor ratio is better, and the ratio is typically calculated using annualized returns and standard deviations.
 
The Information Ratio

The information ratio is used to quantify the value added by active investment managers.
The information ratio is the “alpha” of a portfolio divided by the tracking error. In other words, the information ratio is the excess return relative to a benchmark that a manager generates divided by the extra risk that the manager takes on in order to generate that excess return.
The information ratio is calculated using this equation:

Information ratio=R(P)-Rb/SD=Alpha/SD
 
Conclusion: So it is not only the return which makes portfolio managers stand apart but it is the risk-adjusted return that makes them true genius.