Tickers

Tickers are a standard identifier given to securities to eliminate confusion between securities with similar names, it is a series of 1-5 letters or symbols that correspond to a security. For example: Apples ticker is AAPL, Googles ticker is GOOG etc. You can find the ticker of any security that you would like to invest in simply by searching "what is the ticker for [securities name]" on a web browser.

Expected Return

Expected return is the average return that a stock or portfolio is expected to generate over a given period of time. For example, if a portfolio has an expected annual return of 7%, this means that, on average, the portfolio is expected to grow by 7% per year. It is important to note that this is not guaranteed — it is a statistical estimate based on historical data or modelling.

Variance

Variance measures the volatility and risk of a security, i.e. how unpredictable it is. if a security has an expected return of 2% and a very high level of volatility of 80%, its actual returns could be far above or far below 2% in any given period. This indicates that the security’s performance is highly unpredictable and therefore riskier for investors. There is a payoff between risk and return in investing, it is up to you to decide how much risk and unpredictibility you are comfortable with taking.

Standard Deviation

Mathematically standard deviation is the squareroot of variance, unlike variance it is expressed in the same units as the origional data, i.e. dollars or percent and it allows for comparison between different asset classes. This makes it much easier to interpret and therefore I will always display risk in terms of standard deviation, not variance.

Minimum Variance Portfolio (MVP)

This is one of the 'Optimal' portfolios calculated. It's the portfolio that holds the lowest variance (risk) out of any other possible portfolio that you can create with the securities being invested in. It is very useful for people who want minimal risk for their investment but who want to invest in securites they find promising instead of risk free assets like bonds. It also shows the user the minimum amount of risk that they can hope to achieve given their chosen securities.

Tangency Portfolio (TP)

This is another one of the 'Optimal' portfolios calculated. It's the portfolio that maximises an investors risk-adjusted returns. In other words, In other words, it provides the highest expected return per unit of risk. If you choose to invest on the CAL this is the portfolio you should invest in along side the risk free asset.

Efficient Frontier

This line plots the highest expected return avaliable for each level of risk taken, it is what i will compare your portfolios to to check if they are optimal and tell you how much you can increase your expected return without taking on any additional risk.

Weights

Weights refer to the percentage of your total investment invested in each security, if you wanted to invest $1000 in apple and tesla and you invested 500 in each the weight of apple would be 50% and the weight of tesla would be 50%. Weights can be both positive and negative depending on whether you take a long or short position.

Long position

A long position is when you bet that a security will grow. You take a long position by buying shares, if the price of the shares go up your investment will increase and visa-versa.

Short position

A short position is when you bet against a security, i.e. that its' price will decline. You take a short position by selling a security you do not own through borrowing the security from a broker. Many investors limit or avoid short positions because the maximum loss on a long position is 100% (the investment falls to zero), but the potential loss on a short position is theoretically unlimited, since a stock’s price can continue to rise indefinitely. A well-known example of the risks associated with short selling occurred during the surge in GameStop Corp. shares in 2021, when heavy short positions led to extremely large losses for some investors.

Capital Allocation Line (CAL)

The Capital Allocation Line (CAL) shows the best possible combinations of a risk-free asset and a risky portfolio, in this case, the tangency portfolio, which is considered optimal because it offers the highest expected return for each unit of risk. Your only decision as an investor is how much of your wealth you'd like to invest in the risk-free asset and how much to invest in the risky portfolio. Each point along the Capital Allocation Line represents a different mix of these two investments. The point you choose on the line based on your personal risk tolerance represents your optimal portfolio. It is work noting you can take a short position on the risk free asset and invest over 100% in the risky portfolio.

Risk Free Asset

A risk free asset is an asset that offers a level of return for a negligable level of risk. An example would be a government bond in a finacially stable country. In the presence of a risk free asset the Capital Allocation line becomes the efficient frontier and the minimum variance portfolio becomes 100% invested in the risk-free asset for a portfolio variance of 0. Generally only extremely risk averse investors would put 100% of their investment into the risk free asset