This analysis selects 10 random stocks from different industries listed on London Stock Exchange (LSE) and starts by digesting them with an aim of identifying ideal stocks to form a single ideal portfolio for conservative, aggressive and risk-adjusted optimizers. 

Financial Sector 

1. HSBC

2. Lloyds 

3. Barclays plc 

Energy

1. BP 

Healthcare

1. AstraZeneca 

Consumer & Communication Services

1. Unilever

2. Tesco

3. Vodafone Group

Industrials & Materials

1. BAE Systems 

2. Rio Tinto 

This analysis begins by pulling monthly closing prices for all the stocks in the last 10 years including United Kingdom 10-Year Bond Yield Historical Data, which is used as our risk free rate. Average monthly expected return indicates that BP, Lloyds, Vodafone, Tesco & Unilever lost value in the last 10 years, all with negative return of -0.45%, -0.15%, -1.27%, -0.05% and -0.40% respectively. Similarly, HSBC, Barclays, Rio Tinto, AstraZeneca and BAE Systems gained in value with expected return of 0.10%, 0.40%, 0.29% and 0.41% respectively. 

Based on the historical performance of these stocks, investors who randomly invest in all the 10 stocks with no significant knowledge of the market trends and by allocating equal weight of 10%  to each stock, the value of their investment is likely to drop with an expected return of -0.06%. The risk associated with the investment is 9.91%, which is a very high  risk. The portfolio's average expected return is lower than the risk free rate (0.17%) suggesting that investors would take up a very high risk without rewards.