What is a **risk adjusted return**?

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This simply refers to what you get from an investment taking into account the amount of risk the fund manager has taken.

Example 1. Fund manager A achieves a return of 7% and does so investing in Chinese smaller companys.

Example 2. Fund manager B achieves the same return of 7% but does so using cash, corporate bonds and FTSE100 companys.

So what? Looking just at the return of a share or investment only tells part of the story. It ignores the 'risk' the manager has taken to achieve it.

State four measues you could use to measure the risk adjusted return of a share, investment or portfolio?

1. Sharpe ratio

2. The Captial Asset Pricing Model (CAPM)

3. Information Ratio

4. Alpha

We will look at each of these. AF4 will often have a question on this area.

What is the **sharpe ratio** and what does it measure, i.e what does the formula look like?

It shows the risk adjusted performance of a portfolio or investment in comparison to cash / treasury bills. A high ratio is good as it shows that high returns were achieved without excessive risk taking.

__ return on investment - risk-free return __

standard deviation of the return on the investment

What do we mean when we say **risk-free return**?

Risk-free return is a fundamental concept. It is the expected return to an investor who does not want to take any risk. In practice, this is impossible but UK treasury bills are as close as you will get and for example, 1%.

So, if you only wanted a return of 1%, why would you invest anywhere else?

If you wanted a return of 5%, the only thing investing in UK gilts will guarantee you is a shortfall of around 4%. This wouldn't be smart so in this case, the investor could be said to require a return = the risk-free return + 4%.

What is **alpha**?

What is **beta?**

**Alpha** is the amount by which the fund manager or share out-performs the market generally.

**Beta** measures the sensitivity of a share (volatility) when compared with the markt as a whole. So if the market fluctuates by 3% and a share does the same, it is said to have a Beta of 1. In other words, it follows the market. Tracker funds wil have a beta of 1 (or very close to it).

What is **systemic** (or systematic, or market) risk?

What is **non-systemic** (or non-systematic, or non-market risk)?

The expressions are often used inter-changeably. Use either in AF4.

**Systemic risk is the market risk. **So what? If you are invested in the market, you cannout avoid this risk.

**Non-sytemic risk** is the **risk specific** to the firm or investment. For example, a company makes a poor marketing decision, an oil company has a disaster, fraud is discovered. These will all affect the individual share price of the firms affected. The market, as a whole, will be unaffected.

Why is systematic and non-systematic risk important?

What is **correlation**?

You can reduce or minimise non-systemic risk through **diversification.**

Theory states that you cannot remove or significantly reduce the systematic risk (other than by __not__ being invested in the market).

It is not possible to have diversification without also considering **correlation.** This measures how much one type of asset moves with another. True diversification would have a mix of un-correlated assets.

E.g. the correlation between UK Gov't gilts and the FTSE 100 is said to have a **negative correlation**. Typically, if the FTSE goes up, UK gilts will go down.

What is the formula for measuring **alpha**?

This compares the performance of a portfolio/investment/share against the expected market returns.

It is the actual return, reduced by (the market return - risk free rate of return x the beta of the fund or portfolio + the risk free rate of return)

As a formula this is shown as:

Actual Return - (Rf + Bi (Rm - Rf))

What does the capital asset pricing model (or **CAPM**) suggest?

It says that non-systemic risk **can be **eliminated by market diversification. It is the sensitivity to the market (it's beta) that is important.

This tells us if the investment is worth making in terms of the risk-free return and the amount of risk involved.

What are the main assumptions used for the capital asset pricing model (or **CAPM**)?

Investors are rational and risk averse, making decisions on the basis of risk and return alone.

All investors have an identical holding period.

The market comprises many buyers and many sellers and no one individual can affect the market price.

There are no taxes, no transaction costs and no restrictions on short selling.

Information is free and is simultaneously available to all.

All investors can borrow and lend unlimited amounts of money at the risk-free rate.

What is the **information ratio** and how can we use this?

It measurs the relative returns between an actively managed portfolio and the return from a benchmark (taking risk or volitility into account).

This means it measures risk-adjusted returns, like sharpe ratios and CAPM.

The formula:

__investment return - index return__

tracking error*

*Tracking error = the duifference between returns of the portfolio and the returns of an index.

What are the five main investment theories?

1. Modern Portfolio Theory (MPT)

2. Capital Asset Pricing Model (CAPM)

3, Arbitrage Pricing Theory (APT)

4. Efficient Market Hypothesis (EMH)

5. Behavioural Finance

What is the difference between standard deviation and beta?

Standard deviation measures the volatility of an **individual** **share** **or portfolio**, in comparison to it's historic average.

Beta is also a measure of volatility, but in c**omparison to the rest of the market**

Standard deviation is used in modern portfolio theory, whereas beta is used in CAPM