Evaluating a Collar Strategy for Risk Management

As an investment manager at a large institutional fund, you closely monitor the equity and options markets to execute effective hedging strategies. Currently, your fund holds a significant position in TechCorp, which has seen erratic price movements due to changes in consumer sentiment and interest rate expectations. To manage this risk, you are considering implementing a collar strategy using options on TechCorp's stock.

Given the following information:

• Current stock price of TechCorp: $100
• Strike price of the put option: $90
• Strike price of the call option: $110
• Premium received for the call option: $3
• Premium paid for the put option: $5
• Time to expiration: 6 months

Please discuss the rationale behind the collar strategy, its potential payoffs in various scenarios, the risks involved, and how it aligns with the investment objectives of preserving capital while still allowing for some upside potential. Be sure to include numerical examples for clarity.