A portfolio is a collection of financial instruments. We often collect instruments together to represent the complete holdings of an investor and to analyze the overall risk (which may be lower due to diversification, i.e the portfolio holding multiple instruments).
A portfolio is a collection of financial instruments. Thus it may include securities (stocks, bonds, warrants), derivatives (futures, options, swaps, forwards), hard assets (commodities, real estate, infrastructure), intangible assets (intellectual property, patents), cash (in the investor's home currency), and foreign currencies.
Portfolios may have long holdings as well as short holdings (sometimes represented by negative amounts).
We group instruments into portfolios because they may represent the complete holdings of an investor. We also want to consider the risk of the portfolio -- which may be different than the sum of risks for individual instruments. The overall risk may be lower if some instruments are uncorrelated with other instruments or if the holdings act to cancel out common risk exposures.
There are methods to create portfolios with the minimum risk when holding only risky investments, maximum return per unit of risk, or to invest in an equal amount of risk per instrument. Early work by Markowitz (1952) and Roy (1952) on portfolio optimization sought to maximize the mean return minus some penalty for the portfolio's variance.
Portfolio optimization may consider other risk measures, use stochastic optimization techniques, consider transactions costs, and even account for differences in taxation of gains due to holding periods.