### Project Description

If you are an **investor**, as opposed to a **trader** or **speculator** , it should be understood that there is no way to **manage** investments. Investments will go up, or they will go down, all of their own accord. You have very little to say in the process *(and shouting at the monitor has yet to yield any verifiable benefit).* As an investor, you should look upon yourself as a manager of **risk**. As a manager of risk you will take on the responsibility of first quantifying risk, and then deciding which you wish to take on, and which you wish to avoid. This may sound esoteric to some. The difference between a professional investor and an amateur investor (*think, your friend at work who speculates in penny stocks on his train ride to work Vs. the proprietary trading desk at Goldman sachs….*) can be understood in the answer to the following question:

So what did you answer? If you answer was something along the lines of “the likelihood of losing money” then you are probably not working on the proprietary trading desk of an investment bank. An institutional, or professional definition of “risk” is **unexpected price movement or volatility**

*.*The association with “losing money” is behavioral, and not mathematical. As such, defining risk in such terms offers no useful applications to the risk management process and will likely work as an inhibitor to making rational decisions.

## Risk As Volatility

Volatility can be defined as the rate at which the price of a security increases or decreases for a given set of returns. The investment industry is very fast to point out (*and is legally obligated to do so..) *that, *past performance is not an indication of future returns.* However, we can take a look at volatility to understand how far away from a given set of average returns the asset might move in the future, based on how it has performed so far. If we are able to understand volatility, we are able to understand the likelihood of receiving an unexpected price-movement *(…which could decrease the value of our investment…and cost us money).* *Our* expectation that the **return profile** of the asset remain consistent in the future is a much bigger ask than our expectation of the continuation of its **volatility profile.** We are not speculating as to whether or not the value moves *up* or *down*, simply to the extent of its movements within its range of returns; compared to its average return. Now, the issue with volatility as a measure, is that it does not differentiate between *upward* and *downward volatility. *In fact, we have no complaints whatsoever if an asset shoots up in increments of 15%, despite the volatility profile being extremely high. The asset could similarly **lose value** in 15% increments and the volatility reading would be the same. All else being equal, it is optimal to own a basket of assets which produce positive returns more consistently than negative returns *(Skewness) *and with as small a volatility reading (/V*ariance)* as is possible. Failure to manage volatility will result in variance drain, which will be to the detriment of long-term performance. You are now a part of the professional circle. Risk is volatility. Volatility is risk.

But what is volatility? **Volatility is Standard Deviation.**

## Standard Deviation

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.[1] A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.

Standard deviation is a tool for measuring price volatility or *variance* away from the *mean* performance result. If we have an asset that commonly produces +0.5% each month, in a perfect world we would like it to have 0% volatility so that we can guarantee a return of 0.5% every single month without any deviation away from that performance. Investments with asymmetrically positive return profiles and low volatility are highly sought after. In reality they are very uncommon.

## Simple Risk Budgeting

Now that you have a grasp of **risk as volatility ***(SD=risk)*, you can decide on a **risk budget**. This will enable you take on** smart calculated risk** to grow your investment, within your own parameters. One simple method to do this is the** Constant Proportion Portfolio Insurance** (CPPI) method. To get started you need to know:

1) How much capital you are going to invest

2) How much capital you are willing to lose

3) The SD of the assets that you are looking to buy

Let us imagine the following:

1) Investing 10,000,000 JPY

2) Willing to lose 1,500,000 JPY (15%) over a calendar year in aim of receiving a positive year-on-year return over a 10 year period

3) Looking to allocate money to the S&P500 index, with an annualized volatility of 20%

As we are going to be subjecting 1,5000,000 JPY to risk of loss, 8,500,000 JPY becomes our *absolute floor. *Our efforts will be made to protect this floor. Our loss tolerance level.

The correct amount to be invested in the S&P500 index can be found as (1/0.2) X (10,000,000 – 8,500,000) = 7,500,000 JPY

Accordingly, we can invest the other 4,000,000 JPY into fixed interest securities where we will (*theoretically) *have low variance and nominal capacity for loss (*as long as we hold until maturity*).

**What about when the portfolio grows?**

*Re-balance….*

If the portfolio has grown +20% to 12,000,000 JPY then do the same thing again:

Value: 12,000,000

Willing to risk: 15% of value (= 1,800,000 risk capital)

Volatility of index: 20%

**So:**

(1/0.20) X (12,000,000 – 10,200,000) = 9,000,000 JPY

Meaning our investor would look to rebalance to 9,000,000 JPY in the S&P500 (our risk asset), and 4,000,000 JPY in fixed interest securities.

You should now be able to **quantify the risk of assets,** **determine your risk budget **and use the CPPI method to **build a risk adjusted portfolio**. Understanding the implications of statistical measures like *standard deviation* and *variance *takes little time but enables investors to take meaningful action to reduce portfolio risk. All investors are in agreement that *risk* is a *determinant of return*, but very often not enough is done to plan the manner in which it is taken.

[ Sources ]

– Allianz Global Invesotrs DE: Constant Proportion Portfolio Insurance (CPPI)

– Dynamic Strategies for Asset Allocation, Perold, Sharpe – 1995